Find the number of ways that Magnus can give out $9$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

Answer 1

Since the stickers are identical, the problem can be rephrased as asking for the number of ways to distribute $9$ identical objects to $2$ people. This is a classic stars and bars problem.

Using stars and bars, we can think of the $9$ stickers as $9$ stars and the $2$ friends as $1$ divider. The number of ways to distribute the stickers is then $\binom{9+2-1}{2} = \binom{10}{2} = 45$.

Therefore, there are $45$ ways for Magnus to give out $9$ identical stickers to his $2$ friends.