How many ways are there to choose a unordered box of 12 balls from 21 different balls?

Question

How many ways are there to choose a unordered box of 12 balls from 21 different balls?

I can only think 21 choose 12, but I don't think its right though.

Answer 1

This is sort of the definition of 21 choose 12.

The number of ways to chose the ordered boxes is $21*20*19....*11*10= \frac{21!}{10!}$

But we can divide these into groups of 12! that provide the same unordered bx. Therefore there are $\frac{21}{10!*12!}=\binom{21}{12}$