Donuts and Dividers - Unordered Selections with Repetition [Discrete Math Class]

This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. This is a follow up to previous videos introducing various combinatorial techniques. This current video investigates the method often referred to as "Stars and Bars" to count unordered selections with repetition. We make the case for calling this method donuts and dividers as it shows how to count unordered arrangements of k donuts from n times where repetition is allowed. Along the way, we organize some of the combinatorial techniques we have seen this far (including subsets, permutations, and the product principle).

Note that this video is part of a series kept in a playlist called [Discrete Math Class]:

If you like this video, please consider subscribing to my channel and let me know in the comments if you'd like to see more like this.

This textbook for the course is the open-source textbook by Oscar Levin:

0:00 : Unordered Selections with Repetition
00:08 : Introduction: counting options for a dozen donuts from 10 varieties
00:45 : Counting with and without Repetition
03:06 : Unordered selections with repetition
04:46 : Donuts and Dividers (or Stars and Bars)
05:53 : Two examples
07:05 : Follow up: Counting with and without Repetition

#combinatorics #starsandbars #combinatorialproof #proof #algebraicproof #counting #countingprinciples #binarystrings #productprinciple #donuts #multiplicationprinciple #combinatorialobjects #permutations #subsets #math #manim #discretemathematics #rooks #chessboard #nonattackingrooks

To learn more about animating with manim, check out:

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[harnoor]

Your explanation is exactly what I needed to understand this concept. Thank you for taking the time to create such an informative video.

[xxphoenixx]

This video is so interesting! I'm very bad at math, I have to admit, but your animations really helped me understand some things, even if others still confuse me a bit=) Impeccable job👌

[啦啦啦-zil]

This is so well explained, understand almost immediately

[missingtourist]

So now I know what the guy ahead of me in the DD drive through was doing for so long.

[LUMEN_science]

Wow! the colors and animations are really good!

[yashrawat]

We did this in our Combinatorics class