Awesome! Try doing the problems listed at the bottom of this page. just be careful not to see the solution when you click the problems: artofproblemsolving.com/wiki/index.php/Ball-and-urn
I appreciate the compliment so much. I wish one of the big time math channel blogs would pick up my channel in one of their posts about best math channels, but it seems like they only believe it's one of "the best math channels" if it has 100k subscribers. Some day I guess lol.
Great explanations! I tried working on this problem on my own, but I didn't realize the problem that the exponent for 1 (in your case, z) could be zero, and did the counting wrong. Thanks for the link provided on extra practices for such stars and bars problems! I will make sure I finish them.
Hey! I take the amc 10 on Wednesday and it’s currently Sunday so I really hope you see this before. Im just wondering at 15:16 how did you get 12,560. I tried dividing both the denominator and numerator by 2 in order to get base 2 and use the formula you showed us earlier and I got 49.875. I would really appreciate if you explained how you got your answer, thanks !
Actually the correct calculation is 12,650. I am unsure what I was reading from at the time, but I pulled that number off a piece of paper and it should have been 12,650. The calculation is 25 choose 4 equals 25! Divided by (25-21)!(21!). So the 25 factorial is 25×24×23×22×21!, that 21! Cancels with the denominators 21! This leaves (25×24×23×22)÷(4×3×2×1)=12,650. I am not sure what you mean by dividing both the numerator and denominator by 2 in order to get base 2? Do you mean you are trying to get "n choose 2" formula? You can't divide the choose value in a Combination to create a different combination. You could only do it with the numbers like in the one above I could divide out a 2 from 24 and a 2 from (4×3×2×1) and cancel those...but the Combination has already been calculated at this point. You are simplifying a fraction now. A Combination (25 choose 4) is not a fraction. It cannot be reduced. In addition every combination can only come out to be an integer. Never a decimal. So if you get a decimal, then you made some kind of mistake. Let me know if this helps. I will respond further if you have other questions when time permits. About to start teaching again.
I am teaching until 11pm Tonight Pacific Time, and then going to try and film a last day video for my subscribers before tomorrow and then sleep. I will try and answer this later tonight if I have time, but please don't be sad if I am unable to do so. Thank you for understanding. :)
Hi, TheBeautyofMath(IceMatrix), since the AMC 10A and 10B is happening tomorrow and next Wednesday, I was really hoping to review binomial expansion because I am really bad at that and it would be really nice if you could make a video on it, from easy to hard examples, I know you can't do it before the 10A but it would be really nice if you could do it before the AMC 10B. Thanks. :)
Can you make a video on how to practice reading and understanding questions (I missed that they hadn't included the 1 in the positive condition and got stuck with a different answer). In general, I kind of struggle at interpreting information. Thank you. :)
This is a great idea, sadly I can't remember every question where such things are needed and would require a lot of time going through past tests to find situations where such thinking is applicable. But this will be on a long term to-do list. Thank you for the suggestion.
excellent video too easy to understand!
Very good and well-explained tutorial. It was very helpful, thanks!
Thanks so much for this! This helped me see new ways to use stars and bars!
Thank you so much ❤️😊
Very Welcome Sriram!
Loved it
This video is basically my whole understanding of stars and bars. Thanks for all the help!
Awesome! Try doing the problems listed at the bottom of this page. just be careful not to see the solution when you click the problems: artofproblemsolving.com/wiki/index.php/Ball-and-urn
Great video!! very impressed.
Thank you!
bro, you are probably one of the most underrated math channels on the internet. I really hope everyone will see this content because it is so good :)
I appreciate the compliment so much. I wish one of the big time math channel blogs would pick up my channel in one of their posts about best math channels, but it seems like they only believe it's one of "the best math channels" if it has 100k subscribers. Some day I guess lol.
Thanks! This is so good!
this is really good material, thank you
No problem at all. Thank you for the feedback! :)
your a bless bro this is actually so helpful
Thanks...glad to hear it made a difference in understanding for you. :)
Great explanations! I tried working on this problem on my own, but I didn't realize the problem that the exponent for 1 (in your case, z) could be zero, and did the counting wrong. Thanks for the link provided on extra practices for such stars and bars problems! I will make sure I finish them.
Glad to hear someone found that useful. I just recently added that link. I will try and link more such things in the future when time permits.
Hey! I take the amc 10 on Wednesday and it’s currently Sunday so I really hope you see this before. Im just wondering at 15:16 how did you get 12,560. I tried dividing both the denominator and numerator by 2 in order to get base 2 and use the formula you showed us earlier and I got 49.875. I would really appreciate if you explained how you got your answer, thanks !
Actually the correct calculation is 12,650. I am unsure what I was reading from at the time, but I pulled that number off a piece of paper and it should have been 12,650. The calculation is 25 choose 4 equals 25! Divided by (25-21)!(21!). So the 25 factorial is 25×24×23×22×21!, that 21! Cancels with the denominators 21! This leaves (25×24×23×22)÷(4×3×2×1)=12,650.
I am not sure what you mean by dividing both the numerator and denominator by 2 in order to get base 2? Do you mean you are trying to get "n choose 2" formula? You can't divide the choose value in a Combination to create a different combination. You could only do it with the numbers like in the one above I could divide out a 2 from 24 and a 2 from (4×3×2×1) and cancel those...but the Combination has already been calculated at this point. You are simplifying a fraction now. A Combination (25 choose 4) is not a fraction. It cannot be reduced.
In addition every combination can only come out to be an integer. Never a decimal. So if you get a decimal, then you made some kind of mistake. Let me know if this helps. I will respond further if you have other questions when time permits. About to start teaching again.
@@TheBeautyofMath i get it now, thank you so much!!!
Hello
I was wondering at 27:08 why did you put n!/(n-4)!4! and how did you get to that point?
I am teaching until 11pm Tonight Pacific Time, and then going to try and film a last day video for my subscribers before tomorrow and then sleep. I will try and answer this later tonight if I have time, but please don't be sad if I am unable to do so. Thank you for understanding. :)
SO CLOSE TO 1000 SUBS
Right? I still have to get about 100,000 more watch minutes before partnership. Hopefully in the next couple of months.
Hi, TheBeautyofMath(IceMatrix), since the AMC 10A and 10B is happening tomorrow and next Wednesday, I was really hoping to review binomial expansion because I am really bad at that and it would be really nice if you could make a video on it, from easy to hard examples, I know you can't do it before the 10A but it would be really nice if you could do it before the AMC 10B. Thanks. :)
Yeah, sorry this didn't happen. I will probably do a topical video on this later, but for now I just didn't have the time.
Can you make a video on how to practice reading and understanding questions (I missed that they hadn't included the 1 in the positive condition and got stuck with a different answer). In general, I kind of struggle at interpreting information. Thank you. :)
This is a great idea, sadly I can't remember every question where such things are needed and would require a lot of time going through past tests to find situations where such thinking is applicable. But this will be on a long term to-do list. Thank you for the suggestion.