Whhhhhyyyy doesn't my genetics professor teach it this way??? the formula is so confusing, but the way you explained it I understood it and it's so easy!
My statistics professor is someone who explains things for people who already know about the topic. There are variables everywhere which are not explained. Thank you for making this video, it showed me how simple this actually is and how fun the topic can be.
This is currently the clearest video I've found on permutations. It actually explains the concept behind the equation, which will stay in my understanding far beyond the memory of the equation. Thanks!
Thank you very much, when I learned that at school back then they went over it too fast and I could not get the reasoning behind the formulas. I see clearly now, well presented :-)
I am very grateful for the explanation and logical reasoning. The basic concept is what i really needed and that it something i didn't have while doing additional math for IGCSE. I'm happy nonetheless I have understood in A level statistics. Thank you.
Oh my god thank you so much our teacher has literally taught us nothing about this and has told us to research it for our assignment this helped so much
"And I want to know, how many different ways can I put these 3 balls into these 2 cups?" Call me immature, but I started chuckling. Aside from that, this was very informative.
Thanx khan academy for making the impossible possible coz i am just studying in9th standard and i need to write an olympiad based on 16 chapters which includes combinations and permutations. And now may be i will achieve a good rank in it.
Hi I was very weak in maths I wish internet was super cheap in my academic years I would have got better marks and understanding about maths concepts.Thanks Khan Academy
There are 7 ways of selecting the first person to sit, and FOR EACH way out of the 7 ways, there are 6 ways of selecting the second person. Thus far there 7 * 6 ( = 42) ways of selecting the first two persons and sitting them. Again FOR EACH of the 42 possible ways of selecting the first two persons, there are 5 choices for the third sitter. Eventually we have 42 * 5 ways of selecting 3 out of 7 persons to sit.
i'm with you 100%, bc it irritates me how NO ONE, not even textbooks explain how you just up and multiply. The reason you multiply is just think of what multiplication represents: groups. 7x6 means 7 groups of 6 (or 6 groups of 7). That gives you 42, either way. 3 groups of 2 (or 2 groups of 3) give you 6. Well, if you have say, 4 balls (A, B, C, D) and 3 cups, for your FIRST choice of A, there's 6 ways -6 groups of choices- to fill the 3 cups IF you're starting your choice with A....
Its a drawing pad. You'll also need screen recording software, video editing software, and voice recording software. And a mike. I'm not sure if that software should come with either the mike or the pad.
Reason for multiplying eg you want to go from A --B--C,with three possible routes to B and from B 4 ways to C.for every route to b there are 4 ways to C.total =3*4=12 ways for A to C
I look at this in a much simpler way as below " 3 chairs and 7 people" First spot could be fitted in 7 different way or people in this case. For this 7 different ways of first position there will be 6 different way remaining 6 people can occupy hence 7*6 ways two chair get filled, now again third chair has 5 left over people from each outcome (7*6 total outcomes ). So these 5 will occupy in 5 different way with total outcome of first two chair i.e (7*6)*5. If one more chair is there again we have 4 different ways remaing 4 can be associated with this all possible outcome. By THE WAY mathes is too difficult to explain or visualise through words. Happy learning.
@jarrasoma Well, given i.e. 5 cups and 3 balls - and you put one ball in one cup - you'd have this; Cup 1: Ball A Cup 2: Ball B Cup 3: Ball C Cup 4: No ball Cup 5: No ball Now, there's a problem with our ascertion. Can you see it? The question now is better answered as a relation; In how many ways can you place a cup and a ball together? That way, the places would be the "k", and the other relation would represent the "n".
I got intuitive blast after watching this it made so much sense looking at the angle from that you want the first k terms of the n! Then its almost common sense that you want to cancel out the left terms so you are doing (n-k)! To cancel them (n-k) is number left from n after occupying n spots
So in Braille there are 6 spaces... how many unique characters are there then? Because space 1 and space 2 being filled is the same as space 2 and space 1. Would it just be binary then? 2^6?
hey sal, i'm not understanding this question (it's from iit exam)........ A train timetable must be compiled for various days of the week so that two trains twice a day depart for three days, one train daily for two days, and three trains once a day for two days. How many different timetables can be compiled?......plz answer or better make a video....
So if u have 7 traits, and 2 alleles/ possibilities for each trait. to calculate the possible combinations for 7 traits you would have 14 different traits/people. So your trying to seat 14 different people in 7 chairs/traits so? 14 x 13 x 12 x 11 x 10 x 9 x 8?
+张弼 because you start with 7 people in the 1st chair. after that person sits on the first chair now you only have 6 people or choices left. thats why there are 6 people for the 2nd chair. and for the third chair you have 5 people left. Since there are only 3 chairs we stop here. thus-- 7 times 6 times 5 = 210 possibilities
+DryBlue Berries That's a great question. The key points is "each" "each". As you heard that "for each of these possibilities" ,you probably can imagine that each of the 7 possibilities has another 6 new choices or possibilities. It is like that there are 7 boxes and each box "has" 6 apples, so how many apples are there ? 7 times 6, right?
+张弼 Hey, it seems like ur online right now. Try answering this question: A volley ball team is made up of 6 player in a line facing the camera for a picture. If Joan and Emily must be together, how many different arrangements are possible for the picture?
Could you assist me how could I do a video as above? Including the gadgets need to record this video especially the type of gadgets needed to write like what you wrote. Tq
Out of 18 points in a plane, no three are in a straight line except 5 which are collinear. How many straight lines can be formed & how many triangles can be formed? Sir why do we need to subtract 5c3 from 18c3 in case of triangles
what if k is greator that n, would it just be k! ? for example you are given 22 poeple 23 seats, there are 23! possibilities cause you have to factor in the situation of each time one of the seats is empty but if you had 2 or more would it stay the same or no? because tech the first and the second empty seat would be both equal seats but the 24th seat could still be sat in i just dont know.
A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible? Sir when it asks about sequences that means arrangements why can't we apply this formula 10 p 2 to find the answer ?
In behalf of all the people cramming for their finals right now, thank you!
And here I am, three years later. My final's tomorrow XD
@@Clammychow and here I am, 3 years later. My final's tomorrow xD
@@avory7938 Here I am, a year later. My final is tomorrow.
@@radd4255 I'm here a month later finals tmr
@@yamboyasmr4779 i'm here a month later as well
Whhhhhyyyy doesn't my genetics professor teach it this way??? the formula is so confusing, but the way you explained it I understood it and it's so easy!
Because your genetics teacher isn't an attractive math man
My statistics professor is someone who explains things for people who already know about the topic.
There are variables everywhere which are not explained.
Thank you for making this video, it showed me how simple this actually is and how fun the topic can be.
This is currently the clearest video I've found on permutations. It actually explains the concept behind the equation, which will stay in my understanding far beyond the memory of the equation. Thanks!
I use these videos for my exams at university, just love this. It's no drama if I skip a class, this is taught even better
This is so EASY. I have an exam tomorrow and I'm relying on this video for 5 marks! Extremely helpful!!
Maitri Gandhi how it went?
For others viewing the video:
at 8:00 please note that the factorial symbol should be outside the parenthesis:
n!/(n-k)!
you explained it better than the lecturer at school. thanks for this video :)
Holy shit, this guy does everything! I mean seriously, what can'd he do?
hes a alien here to help us not destroy ourselves
darius jah'skush ALL HAIL THE ALIEN WHOSE VEEN SAVING OUR GRADES!!!
he's an mitian
Adam Dintelman ikr!
Teach badly
Thank you very much, when I learned that at school back then they went over it too fast and I could not get the reasoning behind the formulas. I see clearly now, well presented :-)
THANKS! These are great tutorials, I'm currently doing online schooling and my cousin just recommended you.
In India permutations is taught in class 11 & 12 but due to this awesome guy I understood the topic even after being in class 9 . Thanks Sal
are you in state board ?
I am very grateful for the explanation and logical reasoning. The basic concept is what i really needed and that it something i didn't have while doing additional math for IGCSE. I'm happy nonetheless I have understood in A level statistics. Thank you.
Thank you khan for always bringing me one step closer to smartness.
I usually don't understand his vids, but he taught this so easily... even I could grasp the concept this time 😅
Good explanation. I've always found this sort of thing confusing but this video was very clear. Great intuition gained.
I would like to see Sal teach electrical engineering.
7:58 I feel bad for people watching this on mobile and not being able to see the annotation correction and get really confused
Swiizzey what I'm on mobile pls help
Elias kountouris equation is supposed to be n!/(n-k)!
DeformedBear who the hell allows phones into examination halls
Sal wrote n!/(n-k!)
It's supposed to be n!/(n-k)!
Swiizzey And I certainly did get confused!! Thumbs down for me!!
It is a video from many years before bir it's still very helpul. Thank you so much!
THANK YOU THANK YOU THANK YOU!!!!! I have a probability test next peroid, and didn't get it until I watched this!!!!!
Thank you so much. I've spent an entire day trying to understand this from the textbook with no success.
You explained everything very cleary using easy practical examples. Keep up the good work!
You are the reason I survived 6th grade. thanks for making these videos.
3 balls, 2 cups
You're a life saver!!❤❤❤
2018!? Time flies fast. 2008 passed 10 years back!
Now August 2022 😌🥳
Now end of November 2023. 😌🙏
Oh my god thank you so much our teacher has literally taught us nothing about this and has told us to research it for our assignment this helped so much
Mine did, too! It was the last lesson in the chapter, too xD
***** 8
HermitOfTheFragshack Oh you poor soul I'm in grade 10
+HermitOfTheFragshack me too
me in 2020 tryna understand this topic cause online school doesn't help
I learn more from this than my geometry teacher
"And I want to know, how many different ways can I put these 3 balls into these 2 cups?"
Call me immature, but I started chuckling.
Aside from that, this was very informative.
Thanx khan academy for making the impossible possible coz i am just studying in9th standard and i need to write an olympiad based on 16 chapters which includes combinations and permutations. And now may be i will achieve a good rank in it.
Hi I was very weak in maths I wish internet was super cheap in my academic years I would have got better marks and understanding about maths concepts.Thanks Khan Academy
i am in college and i am learning this all on my own thanks to this guy
Great work sir. Thanks for making me understand this thing so easily.
Wow this style of teaching is soo good
There are 7 ways of selecting the first person to sit, and FOR EACH way out of the 7 ways, there are 6 ways of selecting the second person. Thus far there 7 * 6 ( = 42) ways of selecting the first two persons and sitting them. Again FOR EACH of the 42 possible ways of selecting the first two persons, there are 5 choices for the third sitter. Eventually we have 42 * 5 ways of selecting 3 out of 7 persons to sit.
@moka22051 A factorial is when you multiply that number by all the positive integers below it. For example, 7! is 7*6*5*4*3*2*1.
Been sitting in a chair for 2 hours, but I've never understood it. Now, 10 minutes and I have understood at least a tinsy bit.
i'm with you 100%, bc it irritates me how NO ONE, not even textbooks explain how you just up and multiply. The reason you multiply is just think of what multiplication represents: groups. 7x6 means 7 groups of 6 (or 6 groups of 7). That gives you 42, either way. 3 groups of 2 (or 2 groups of 3) give you 6. Well, if you have say, 4 balls (A, B, C, D) and 3 cups, for your FIRST choice of A, there's 6 ways -6 groups of choices- to fill the 3 cups IF you're starting your choice with A....
Khan Academy rules...
Wig snatched. Thanks Sal, I needed this refresher (found an application for it in my research so many years later lol).
Its a drawing pad. You'll also need screen recording software, video editing software, and voice recording software. And a mike. I'm not sure if that software should come with either the mike or the pad.
great explanation ... a good analogy might be scrabble tiles on the rack played on the board squares...
THANK YOU REALLY MUCH, I have tomorow big math exam, it helped me a lot
So , how was the exam?
old but gold
Reason for multiplying eg you want to go from A --B--C,with three possible routes to B and from B 4 ways to C.for every route to b there are 4 ways to C.total =3*4=12 ways for A to C
I look at this in a much simpler way as below
" 3 chairs and 7 people"
First spot could be fitted in 7 different way or people in this case.
For this 7 different ways of first position there will be 6 different way remaining 6 people can occupy hence 7*6 ways two chair get filled, now again third chair has 5 left over people from each outcome (7*6 total outcomes ). So these 5 will occupy in 5 different way with total outcome of first two chair i.e (7*6)*5. If one more chair is there again we have 4 different ways remaing 4 can be associated with this all possible outcome. By THE WAY mathes is too difficult to explain or visualise through words. Happy learning.
@jarrasoma
Well, given i.e. 5 cups and 3 balls - and you put one ball in one cup - you'd have this;
Cup 1: Ball A
Cup 2: Ball B
Cup 3: Ball C
Cup 4: No ball
Cup 5: No ball
Now, there's a problem with our ascertion. Can you see it? The question now is better answered as a relation; In how many ways can you place a cup and a ball together? That way, the places would be the "k", and the other relation would represent the "n".
I got intuitive blast after watching this it made so much sense looking at the angle from that you want the first k terms of the n! Then its almost common sense that you want to cancel out the left terms so you are doing (n-k)! To cancel them (n-k) is number left from n after occupying n spots
Thank You, actually i had a Pre-Algebra book and i couldnt understand it, but with the video i could
Thank You your videos are awesome for online school.
I'm doing this in 7th grade SOO... This is REALLY helpful
Quality is a concern over here when you watch online. But if you download the same & watch it with VLC player, clarity is superb...:)
Great video!! keep it up... better than my math teacher
idk how you know so much...thanks alot man!! :) really helped
this video is such a great help, thank you
the quality of the video is amazing
thanks Khan your vid's help so much ☺☺☺
Thanks, your videos are always great!
At 7:55 , it is n!÷(n-k)!
Гленн Борс you sir are correct. please note everyone. it is NOT n!/(n-k!)
this guys lessons are awesome
Yeah dey ma be techen stu nonsence
I just found a link of his RUclips channel in my textbook...I mean I love videos so I got curious. And I don't regret I did that.
Thankss KA!! gosh ur the bestt!! i totally understand this now!!
Thankyou sir I really respecte what you for us Teens and Kids
omg thank you so much i might just pass my public exam with this (":
Thank you for making this so understandable!
You save my life thank you so much really
Wonderful Explanation !
This helped me a lot!
So in Braille there are 6 spaces... how many unique characters are there then? Because space 1 and space 2 being filled is the same as space 2 and space 1. Would it just be binary then? 2^6?
Hey, I think you should put that factorial sign of k outside the braces in 8:04
Better than my math teacher
The first person that makes sense.
how many 4-digit numbers can be formed from the digits 1,3,5,6,7,8 & 9 if no repetition is allowed?
help pls
7*6*5*4= 840
Marian Frac 840
Very well explained!
Thanks for the subtitles, kid.
what do you mean by w/o restriction? example?
hey sal, i'm not understanding this question (it's from iit exam)........ A train timetable must be compiled for various days of the week so that two trains twice a day depart for three days, one train daily for two days, and three trains once a day for two days. How many different timetables can be compiled?......plz answer or better make a video....
This helped me allot!
So if u have 7 traits, and 2 alleles/ possibilities for each trait. to calculate the possible combinations for 7 traits you would have 14 different traits/people. So your trying to seat 14 different people in 7 chairs/traits so? 14 x 13 x 12 x 11 x 10 x 9 x 8?
please do combinations with repetition! it would be greatly appreciated! :D
oh thank you. real kind of u mr. old guy.
why should we multiply the 7×6×5 ?Is there any intuition explanation?
+张弼 because you start with 7 people in the 1st chair. after that person sits on the first chair now you only have 6 people or choices left. thats why there are 6 people for the 2nd chair. and for the third chair you have 5 people left. Since there are only 3 chairs we stop here. thus-- 7 times 6 times 5 = 210 possibilities
+pinkie24 but why not add?
+DryBlue Berries That's a great question. The key points is "each" "each". As you heard that "for each of these possibilities" ,you probably can imagine that each of the 7 possibilities has another 6 new choices or possibilities. It is like that there are 7 boxes and each box "has" 6 apples, so how many apples are there ? 7 times 6, right?
+pinkie24 thank you every much. After about a week of thinking and practice, I think I get it.
+张弼 Hey, it seems like ur online right now. Try answering this question: A volley ball team is made up of 6 player in a line facing the camera for a picture. If Joan and Emily must be together, how many different arrangements are possible for the picture?
how many four digit no with diff digit can be formed if unit and thousands digit must be prime?
an oldie but a goodie
Did it bother anyone else at the beginning of the video where he didn't have a whole line over the 2? Maybe it's just my OCD again...
+Chill Edits lol
I didnt realize that until now. Thanks for making me annoyed
The bigger problem is the unclosed six at the left center
Yeah, It annoyed me for a sec. Then I realized, oh, he must be using a Windows XP machine. lol Man!! His videos has sure come a long way.
Here in 2022, best lectures👍
In the first example with the 3 chairs why would we use npr? Npr is for when order manners. How does order manner here???
Could you assist me how could I do a video as above? Including the gadgets need to record this video especially the type of gadgets needed to write like what you wrote. Tq
How do you do it? What is this software?
Thankyou very much, It is really Helpful
Keep making awesome videos like these.
I'm here in preparation for my licensure examination.😆
Out of 18 points in a plane, no three are in a straight line except 5 which are collinear. How many
straight lines can be formed & how many triangles can be formed?
Sir why do we need to subtract 5c3 from 18c3 in case of triangles
What if you have just one chair and you can only fit like 4 people? Need help on this
@ninjaturtle205 lol a brown ball n yello ball too and he puts them on the cups!
what about putting all the ball in one cup? is that not a possible scenario
what if k is greator that n, would it just be k! ? for example you are given 22 poeple 23 seats, there are 23! possibilities cause you have to factor in the situation of each time one of the seats is empty but if you had 2 or more would it stay the same or no? because tech the first and the second empty seat would be both equal seats but the 24th seat could still be sat in i just dont know.
1337wOn, what brand of drawing pad do you recommend. Thank you
thx! it helped me very much!
A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two
candidates wrote the answers in an identical sequence. How
many different sequences of answers are possible?
Sir when it asks about sequences that means arrangements why can't we apply this formula 10 p 2 to find the answer ?