Originally Posted by

**sunmalus** there are k bags numbered from 1 to k ( you can tell the difference between the bags), and you have n balls ( you can't make the difference between the balls). also $\displaystyle k \leq n $

a)how many possibilities you have of putting all the balls in the bags with each bag having at least 1 ball in it.

b)how many possibilities you have of putting all the balls in the bags.

My answers

a)$\displaystyle \binom{n-1}{k-1}$

b) $\displaystyle \binom{n+k-1}{k-1}= \binom{n+k-1}{n}$