Q:

Multiset - double binomial coefficient?

In a recent question I have seen for the first time the symbol in my life:
$$\left(\!\!{n\choose k}\!\!\right)$$
Practically why this symbol is used and what are the benefits in the mathematical-informatics area? I didn't really understand it much having given it a quick read. Could it be useful for me as an application of a high school concept or as an application example?
Related link: https://en.wikipedia.org/wiki/Multiset

A:

As your reference states, it is sometimes used to count the $k$-element multisets from a base set of size $n$. E.g. $\left( \binom{10}{12} \right)$ counts the (essentially different) ways in which you can pick up a dozen assorted donouts if the store carries 10 different types of donuts. If the store carries just one type, it is $\left( \binom{1}{12} \right) = 1$, if they carry two, it is $\left( \binom{2}{12} \right) = 13$ (from 0 of the first type to 12 of it), and so on.
Not very common, but not unheard of either. And the notation isn't exactly standard.

