+729 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.)
+1365 We can use stars and bars to solve this problem.
We have 9 stickers in a row (stars)
We need to split these 9 stickers into two groups. We can use one bar for this.
We have something like this
X X X | X X X X X X
In this case, one friend gets 3, the other gets 6.
Now, the problem becomes, how many positions can the bars be put in.
We have \(10 \choose 1\) = 10, so there are 10 ways.
Thanks! :)
