Not really. A great teacher would have put the formula into context and made it more accessible. And don't go saying that it should've been understood from the start because then what's the teacher for?
For people who dont know why factorials calculate arrangements, this is how my teacher explained it that i thought was really good: So imagine we have 3 counters. Red, blue, and green. We need to arrange them, and we do so by selecting one at a time. For the first selection, there are 3 possibilities, one for each colour. On the second round, there are 3 possibilities, minus the one we already chose. So 3-1=2 possibilities. If you remember, we find the total number of outcomes by multiplying the number of outcomes from each stage together, say when you toss a coin twice there are two outcomes for each stage, so 2*2 outcomes, which is 4. HH, HT, TH, TT. We do that here. So when we do our final stage, there is only one choice, so our total outcomes is 3*2*1, or 3!
A very frequently asked question based on sub factorials (derangement) that is asked in many aptitude exams in India is this - Suppose there are 5 letters and 5 envelopes. In how many ways can you put the letters in the envelopes so that none of the letters reach its intended destination. The answer to this problem is simply !5, which is 44. Great video Andy ;)
Finished calculus 3 and just found out factorials are how many ways you can arrange that many things. I don't know how I never mentally connected those
@@davidwu8951I learned about factorials in the context of probability calculation and I still only now figured that out thanks to the video. I finished school in 2018
This is the style of teaching that's straight to the point that would've made me actually put effort in my calculus classes. This makes it accessible, fun, and memorable. In 3 minutes I properly learned about factorials and subfactorials, and can sum them up for a random person on the street. And the best part is I'm confident that I'll remember the concept years from now just because of this explanation!
Never heard them being called 'sub factorials' before. In my 11th grade maths class, we call this 'Disarrangement', but its the same thing. Cool to know that it is called this too! Will definitely info-drop this with my classmates!
This is the sort of thing I'm delighted to learn exists, especially that there's a closed form. Also, your calculated example was super-pedantic, which I really appreciate, because if I tried the closed form on my own, I'd probably make an arithmetic error :( Thanks!
Thanks for making these videos! This was so easily understandable, I used to sit in Probability class and finish the session without understanding a single thing SMH, really wish I had access to youtube back then, would've done so much better in math and physics subjects.
Great explanation! The very first time I ever heard of factorals was in an explanation that if you shuffle a deck of cards you are very likely to have been the very first person to have shuffled that combination. As I recall it was !51, which is an unimaginably large number. Had these fun factoids or an explanation as succinct as yours been in my high school I might have been more interested in the subject.
Thank you! I learned something new. I've approached problems that were described by this in my work but never knew how to describe it. I'd just solve it the long way in Excel.
Damn, calculus is amazing. A shame I never learned it at schol because somehow, my country decided it's not important to be teached at high school. This shit is awesome
Your spirit is really amazing but unfortunately this isn't calculus😅 if you want there are tons of resources online for free to study calculus and multivariable calculus you can actually get Full courses (with exams and assignments and lectures and sections...etc) from MIT Open courseware
It's not calculus, it's combinatorics. Also there's a lot of people who won't use calculus concepts directly in their lives, so it would be pointless to teach it at high schools. For us that do like math, we can always use the internet to learn more stuff than what is taught in the school.
Back when I went to school, this was covered in Discrete Mathematics. I know we also covered it in high school, but it might have just been a general advanced math class? Combinatorics can serve a purpose in common life situations (ok, not super common, but still useful at times).
@@nech060404 Everybody uses calculus in the sense that it is necessary to engineer the devices we use in our daily lives. Not everybody have to know how to calculate an integral though, just like not all mathematicians have to know what was the Nanjing massacre, how to speak portuguese or how to improve a website SEO. Different jobs for different people requires different skills.
As someone with only a high school understanding of math, the subfactorial topic is neat and all, but seeing someone finally explain what ∑ means is probably invaluable. Thank you. It means 'add everything between the number under ∑ and the number over ∑,' right? Did I interpret that correctly?
Yes, you are correct. You start from whatever the variable under the sigma, in this case k, is equal to and you substitute that value of k into the equation that comes after the sigma. when you have this, you increment k by 1 and do the same thing to get a new number and add the two numbers together. Keep on doing this until your value of k matches the number above the sigma.
i put this on my watch later list when I got this video recommended to me (which was not long after it released) but never watched it. Now that I did, I don't know why I didn't do it earlier. Pretty neat
Brit in the UK. Despite having A-Level maths and doing the first year of an Astrophysics degree, before switching to Chemistry. This is the first time I've heard of subfactorials. Thank you for the fascinating video.
Yeah im finishing my physics degree this year and I have genuinely never heard of them. Perhaps they're not important to my specialization, or simply i've been using derivations. real cool thing to know, though.
I had not heard of subfractionals and went in deep after watching this video. And of course, a wild e appeared. The limit as n approaches infinity of !n/n! is 1/e. How exciting.
I've never knew about Subfactorials, that's really cool. I'm curious on use cases for it? When would I want to eliminate an arrangement that has items in already matched positions? Obviously, math is based on the abstract generic usage, but I'd love to see an example (word problem) of Subfactorial.
I have BA in mathematcs and I just learned something. I also enjoyed your clear presentation - subscribing! (No, that's not the factorial of "subscribing")
I love the way mathematicians explain the methodology so precisely, yet fail to even hint at what it’s actually useful for. This is why people don’t get maths.
"For what is poetry good?" Do you need a reason? Marh is beautiful for itself, although it is used for practical reasons too. Memorizing a poetry is good for exercising your memory, but that's not why it was created. Math is like a sculpture, sometimes we take too much marble, sometimes too little, but the statue is there, waiting to be revealed.
If you want to compute it quickly, just round n!/e to the nearest integer. (Which tells you also that a random permutation has about 1/e chances to have no fixed point.)
I did it like this: n! is Γ(n+1) = Γ(n+1, 0) for n being a natural number. (I always say it's equal, but the definition says it's not. qwq) !n is Γ(n+1, -1)/e. Γ(n, x) is the incomplete gamma function which is defined as the integral from x to infinity of t^(n-1)*e^-t dt. For odd n and negative t, t^(n-1)*e^-t is negative. when n=3 and t
Subfactorials count the derangements of a list of items. Derangements are the permutations of the items when each item is out of its original place. Lets say you have a list ABCD. So a derangement of those items will count the permutations when A is not on first place and B is not on second place and C is not on third place and D is not on fourth place. The derangements of ABCD are BADC BCDA CADB CDAB CDBA DABC DCAB DCBA
I see many people who know calculus being surprised by the use of factorials in arrangement of stuff. I'm curious, were you all not taught permutations and combinations simultaneously, before or after calculus?
I covered factorials when I learned about series in calculus. However, I didn’t cover permutations and combinations until I got to discrete math in college.
@@K1JUY Interesting, though I can see how teaching only upto Taylor series would be sufficient for basic calculus, though for me P&C was taught before calculus so that our algebraic grasp would be concrete.
I never liked math until i dropped out of college, now i solve math equations from my younger brother's booksfor fun. I would love to go back to study now.
Not going to lie, right after Andy said “this one has the exclamation after, this one has it before…” I was fully expecting him to say “How Exciting” and the video to end 8 seconds in. Lmao. 😂
Can you please use a black (or dark grey) backhround and white (or light grey) text? It would be much easier to look at the screen. Thank you, and keep up the good work )
But isn't it kind of weird, how the Factorial counts the original ABC-permutation, whereas the subfactorial doesn't? So, at least from the verbalexplanation, I feel like !3 should be 3, not 2
How many ways can you arrange the individual letters A, B, and C? 6 ways, one of the ways is ABC. How many ways can you scramble the string of letters "ABC"? Only 2 ways because "ABC" is not a scrambled version of "ABC."
Good time of year to release this video. Derangements can be used to work out the probably of a Secret Santa draw _not_ working i.e. What are the chances that someone in the office will draw out _their own name_ from the hat?!
The way you speak is bizzare. When you end a sentence sometimes you say it like your losing your voice or momentum. It's always on the same note too. Idk maybe I'm the weird one for analyzing people's speaking patterns lol.
How exciting
How exciting
How exciting !
How exciting!
This comment looks important so let’s put a box around it
How exciting
Never heard of sub factorials before, very fun!
exciting*
@@LiriosyMas you're right, I can't believe I made such a rookie mistake!
Me too
yeah!
how exciting
Subfactorials basically tell you how many different ways you can completely re-arrange a set of objects
thanks, that explanation is way more clear
What do you mean by ‘completely’?
@@alex.g7317 such that no object remains in its original position.
@@The_Story_Of_Us ah, right… I always wondered what use having sub factorials can have. Do you know any uses?
@@alex.g7317 I’d only be guessing the obvious really.
hard time learning math? this guy helps u by explaining almost every equation and formula and gives examples of it. overall 5 stars math teacher
:)
Not really. A great teacher would have put the formula into context and made it more accessible. And don't go saying that it should've been understood from the start because then what's the teacher for?
Calm down br @@denhurensohn9276
For people who dont know why factorials calculate arrangements, this is how my teacher explained it that i thought was really good:
So imagine we have 3 counters. Red, blue, and green. We need to arrange them, and we do so by selecting one at a time. For the first selection, there are 3 possibilities, one for each colour. On the second round, there are 3 possibilities, minus the one we already chose. So 3-1=2 possibilities. If you remember, we find the total number of outcomes by multiplying the number of outcomes from each stage together, say when you toss a coin twice there are two outcomes for each stage, so 2*2 outcomes, which is 4. HH, HT, TH, TT. We do that here. So when we do our final stage, there is only one choice, so our total outcomes is 3*2*1, or 3!
Well explanation but I didn't understand a sht may be my English weak
@@Allena_boofe is it your second language? feel free to ask me any questions abt it im happy to try explain differently.
@@meks039 yes please explain me if you can
@@meks039 it would be very greatful for me
@@Allena_boofe okay so is there anything specific you dont quite get? just copy paste in the bits where you lost track if you dont get it.
A very frequently asked question based on sub factorials (derangement) that is asked in many aptitude exams in India is this -
Suppose there are 5 letters and 5 envelopes. In how many ways can you put the letters in the envelopes so that none of the letters reach its intended destination.
The answer to this problem is simply !5, which is 44.
Great video Andy ;)
Finished calculus 3 and just found out factorials are how many ways you can arrange that many things. I don't know how I never mentally connected those
Not sure if you’ve ever used factorials for calculating probability but it’s a way to closely connect the two!
@@davidwu8951I learned about factorials in the context of probability calculation and I still only now figured that out thanks to the video. I finished school in 2018
It was in discrete math (or combinatorics - seen it called both in different schools) where I learned that
I literally used them for a chapter in combinatrics wnd never realised.
So THAT’S why 0! is equal to 1. Mind blown
This is the style of teaching that's straight to the point that would've made me actually put effort in my calculus classes. This makes it accessible, fun, and memorable. In 3 minutes I properly learned about factorials and subfactorials, and can sum them up for a random person on the street. And the best part is I'm confident that I'll remember the concept years from now just because of this explanation!
Math can be really fun if explained properly. I wish I had a teacher like you when I was learning things.
Never heard them being called 'sub factorials' before. In my 11th grade maths class, we call this 'Disarrangement', but its the same thing. Cool to know that it is called this too! Will definitely info-drop this with my classmates!
You gotta admit that 'derangement' sounds funnier.
Well we call it 'dearrangement' dk if it's a word or not tho
I love the animations, they aren't fancy stuff so it's easy to keep track of where the values go or how they change. Amazing video.
In the formula you can also start at k=2 for any !x where x>1 just because the first two terms always cancel out.
I’ve never thought about factorials as arranging things. Cool way to think of it. Thanks for the informative vid man
This is the sort of thing I'm delighted to learn exists, especially that there's a closed form.
Also, your calculated example was super-pedantic, which I really appreciate, because if I tried the closed form on my own, I'd probably make an arithmetic error :(
Thanks!
I knew about combinations and permutations but not this secret third thing. Neat!
I don’t know if I ever learned this, but very fascinating. Thanks for the knowledge
Thanks for making these videos! This was so easily understandable, I used to sit in Probability class and finish the session without understanding a single thing SMH, really wish I had access to youtube back then, would've done so much better in math and physics subjects.
Great explanation! The very first time I ever heard of factorals was in an explanation that if you shuffle a deck of cards you are very likely to have been the very first person to have shuffled that combination. As I recall it was !51, which is an unimaginably large number. Had these fun factoids or an explanation as succinct as yours been in my high school I might have been more interested in the subject.
Your simple style, fun equations, and obvious interest in math made me subscribe 💯
You mean exciting
There is no fun in math, only an abyss
Its really appreciable someone teaching maths in terms of how its used.
Never knew i was a math nerd until i started seeing ur videos on insta and now im here. How exciting
Dang! Clear and clean explanation. No fluff, no carryon. Nice. 👏
Thank you! I learned something new. I've approached problems that were described by this in my work but never knew how to describe it. I'd just solve it the long way in Excel.
The fact that he is so cute and pretty makes his videos so much better
Your explanation are very exciting! Thanks to you, I finally understand Summations!!! Thank you!!!
you are by far the best teacher
Why does the subfactorial formula's sum start from 0 instead of 2?
Damn, calculus is amazing. A shame I never learned it at schol because somehow, my country decided it's not important to be teached at high school. This shit is awesome
Your spirit is really amazing but unfortunately this isn't calculus😅 if you want there are tons of resources online for free to study calculus and multivariable calculus you can actually get Full courses (with exams and assignments and lectures and sections...etc) from MIT Open courseware
It's not calculus, it's combinatorics. Also there's a lot of people who won't use calculus concepts directly in their lives, so it would be pointless to teach it at high schools. For us that do like math, we can always use the internet to learn more stuff than what is taught in the school.
Back when I went to school, this was covered in Discrete Mathematics. I know we also covered it in high school, but it might have just been a general advanced math class? Combinatorics can serve a purpose in common life situations (ok, not super common, but still useful at times).
@@Israel220500 I disagree we should require everyone to use calculus. Calculus is the study on how things change in systematic ways.
@@nech060404 Everybody uses calculus in the sense that it is necessary to engineer the devices we use in our daily lives. Not everybody have to know how to calculate an integral though, just like not all mathematicians have to know what was the Nanjing massacre, how to speak portuguese or how to improve a website SEO. Different jobs for different people requires different skills.
Freaking cool, bro! I’m gonna use these things in Scholars Bowl 😂
So 8 years of Andys Math videos. How exciting.
As someone with only a high school understanding of math, the subfactorial topic is neat and all, but seeing someone finally explain what ∑ means is probably invaluable. Thank you.
It means 'add everything between the number under ∑ and the number over ∑,' right? Did I interpret that correctly?
Yes, you are correct. You start from whatever the variable under the sigma, in this case k, is equal to and you substitute that value of k into the equation that comes after the sigma. when you have this, you increment k by 1 and do the same thing to get a new number and add the two numbers together. Keep on doing this until your value of k matches the number above the sigma.
yep. Its a sum :)
first time hearign about subfactorial but this was pretty cool and kept my attention throughout
i put this on my watch later list when I got this video recommended to me (which was not long after it released) but never watched it.
Now that I did, I don't know why I didn't do it earlier.
Pretty neat
I did all the advanced level maths in high school. During finite math (combinations and permutations) we were never told about subfactorials.
Brit in the UK. Despite having A-Level maths and doing the first year of an Astrophysics degree, before switching to Chemistry. This is the first time I've heard of subfactorials. Thank you for the fascinating video.
Yeah im finishing my physics degree this year and I have genuinely never heard of them. Perhaps they're not important to my specialization, or simply i've been using derivations. real cool thing to know, though.
I had not heard of subfractionals and went in deep after watching this video. And of course, a wild e appeared. The limit as n approaches infinity of !n/n! is 1/e. How exciting.
figures.
i like math but i’m not good at it, so desmos’ graphing calculator is a good friend of mine.
so i randomly did !x/x! and silently cried
Dude I just did the same thing but the other way around. That actually kinda funny lol.
I love all math and I’ve never heard of a subfactorial. Makes perfect sense . Thx
Man this was amazing!!, loved the video
I learned so much in this video, you have no idea.
I've never knew about Subfactorials, that's really cool. I'm curious on use cases for it? When would I want to eliminate an arrangement that has items in already matched positions? Obviously, math is based on the abstract generic usage, but I'd love to see an example (word problem) of Subfactorial.
I haven’t needed to know this since 2002 or something. Why is this so interesting? I won’t need it again until my kid asks me math questions.
I have BA in mathematcs and I just learned something. I also enjoyed your clear presentation - subscribing! (No, that's not the factorial of "subscribing")
Awesome, thank you!
Missed opportunity to talk about other proofs for 0! = 1, but i guess they might end up in another video. That would be very
exciting
What a pitty
How exciting
Eddie Woo has made a video about that
I love the way mathematicians explain the methodology so precisely, yet fail to even hint at what it’s actually useful for. This is why people don’t get maths.
"For what is poetry good?" Do you need a reason?
Marh is beautiful for itself, although it is used for practical reasons too. Memorizing a poetry is good for exercising your memory, but that's not why it was created.
Math is like a sculpture, sometimes we take too much marble, sometimes too little, but the statue is there, waiting to be revealed.
@@clownphabetstrongwoman7305 Interesting take there. My comment was mostly just sarcasm, but I appreciate your viewpoint as well.
the factorial explanation made me drop the like best way to explain what's a factorial
Mathematicians: Uhh its too long to write.. let's shorten it!
*Random RUclipsr: Content!!!*
I thought that it's gonna be a bigger version of factorials like [ exponentiation --> tetration ], but ok I learned something.
Cool video but just wanted to say because I realised it and can't unsee it, your outfit looks almost exactly like Terry Davis
What a great recursive formula for derangement. reminds me of dynamic programming techniques.
This is new to me and very interesting.Thanks Andy
Easily explained a bit of permutations and derangements too!
Great😊
Really commendable 🎉
Finely understanding why factorial 0 == 1, because of arrangements of course !!! Good explanation man, thank's a lot. 👍👍👍.
This is actually a good piece of knowledge to have, might be useful one day
Factorials are very useful in a number of situations, like probability, sorting, etc. What is the use of subfactorials?
I am interested too.
Best explanation I've seen for this - Good job Mr. Math.
If you want to compute it quickly, just round n!/e to the nearest integer. (Which tells you also that a random permutation has about 1/e chances to have no fixed point.)
The 1st time I learned factorials was in ICS 111 @ Honolulu Community College decades ago.
I did it like this:
n! is Γ(n+1) = Γ(n+1, 0) for n being a natural number. (I always say it's equal, but the definition says it's not. qwq)
!n is Γ(n+1, -1)/e.
Γ(n, x) is the incomplete gamma function which is defined as the integral from x to infinity of t^(n-1)*e^-t dt.
For odd n and negative t, t^(n-1)*e^-t is negative. when n=3 and t
Subfactorials count the derangements of a list of items.
Derangements are the permutations of the items when each item is out of its original place.
Lets say you have a list ABCD.
So a derangement of those items will count the permutations when A is not on first place and B is not on second place and C is not on third place and D is not on fourth place.
The derangements of ABCD are
BADC
BCDA
CADB
CDAB
CDBA
DABC
DCAB
DCBA
I see many people who know calculus being surprised by the use of factorials in arrangement of stuff. I'm curious, were you all not taught permutations and combinations simultaneously, before or after calculus?
I covered factorials when I learned about series in calculus. However, I didn’t cover permutations and combinations until I got to discrete math in college.
♥️♥️
With love
@@K1JUY Interesting, though I can see how teaching only upto Taylor series would be sufficient for basic calculus, though for me P&C was taught before calculus so that our algebraic grasp would be concrete.
I never liked math until i dropped out of college, now i solve math equations from my younger brother's booksfor fun. I would love to go back to study now.
that explanation was really easy to follow!
This is something they never mentioned to me at school. Fascinating! 👍
very nice ! today i have learned sth new. thanks sir
Reminds me of a free group action. All the nonidentity permutations are derangements.
Exciting....so much exciting!
My mind is blowing, this is so exciting!
The way you teach me is really awesome man ❤
Thanks! First mathematical explanation on sub-factorial
Can we write 5!5=?
You probably need to use parentheses
This is how you can compute how many different ways you can have a secret Santa gift exchange arranged with n people.
Not going to lie, right after Andy said “this one has the exclamation after, this one has it before…” I was fully expecting him to say “How Exciting” and the video to end 8 seconds in. Lmao. 😂
I can't even start to imagine Grahams number factorial.
You forgot about factorials and sub factorials of fractions! That's where the fun is!
Can you please use a black (or dark grey) backhround and white (or light grey) text? It would be much easier to look at the screen. Thank you, and keep up the good work )
Your are a damn good teacher😂 thanks man
How exciting - indeed? And yet, you made it interesting.
You explained so clearly. Thank you. It was interesting!
no one has ever said that factorials are ways you can arrange a set and i was always a bit ticked no one mentioned it.
That was honestly exciting. Today I learned something new. (:
But isn't it kind of weird, how the Factorial counts the original ABC-permutation, whereas the subfactorial doesn't? So, at least from the verbalexplanation, I feel like !3 should be 3, not 2
I was also thinking the same thing.
Someone please answer this question
How many ways can you arrange the individual letters A, B, and C? 6 ways, one of the ways is ABC.
How many ways can you scramble the string of letters "ABC"? Only 2 ways because "ABC" is not a scrambled version of "ABC."
now i know how to rearrange people around a table if nobody likes where they're seated
We need to bring back the 0.5 factorial videos 😂
Good time of year to release this video. Derangements can be used to work out the probably of a Secret Santa draw _not_ working i.e. What are the chances that someone in the office will draw out _their own name_ from the hat?!
Amazing! I have never ever heard of this before.
Are there any applications for subfactorial?
Great video, simple and clear message.
New sub :)
Thank you, now i know the principles of sum too 😂😂😂
The way you speak is bizzare. When you end a sentence sometimes you say it like your losing your voice or momentum. It's always on the same note too. Idk maybe I'm the weird one for analyzing people's speaking patterns lol.
The subfactorial 3 (!3) looks like a winking :3
you're the first person I've found that explained why 0! is 1
remember having to do these for high school statistics. It works very well for probably.
Best final words ever
Would've been hilarious if the video ended at 0:07 lmao
Thanks dude was very interesting you’re getting a sub.
Great video, I understood it completely and it has a great pacing
Excellent!!
This video is a bomb
Subfactorials are so cool. Can you explain Tetration too?
I was excepting subfactorials to basically just be dividing each number (so n/((n-1)!) but boy was I wrong