Discrete Mathematical Structures, Lecture 1.5: Multisets and multichoosing.

Discrete Mathematical Structures, Lecture 1.5: Multisets and multichoosing.

A multiset is like a set but repetitions are allowed. An example of a counting problem involving a multiset is to enumerate the number of ways there are to buy k drinks from a vending machine with n flavors. In this lecture we see how to represent multisets using the classic "stars and bars" notation, and how to enumerate the number of size-k multisets formed from an n-element set. We compare this to the other 3 types of problems that we have seen: enumerating sets without repetitions (i.e., combinations), lists without repetition (i.e., permutations), and sets with repetitions allowed (counted by n^k).

[janit]

at 11:41, isn't it supposed to be k stars and n-1 bars

[quantstyle]

How are there k-bars when k = 9 and you drew 4 bars? But aside from that, this is great!

[samparkour]

Can I please get help with this question:
Find the number of 5-permutations of the set (∞a, ∞b, 3c)