Find the number of ways that Magnus can give out $9$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

Answer 1

We can use stars and bars to solve this problem.

Since each friend must receive at least one sticker, we can give one sticker to each friend initially, leaving $7$ stickers left to distribute. Now, we have $7$ indistinguishable objects (the stickers) and $2$ distinguishable containers (the friends).

By stars and bars, the number of ways to distribute the $7$ stickers among the $2$ friends is ${7+2-1 \choose 2-1} = {8 \choose 1} = 8$.

Therefore, Magnus can give out the $9$ stickers in $8$ different ways.