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.)

eramsby1O1O Jun 7, 2024

#1**+1 **

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! :)

NotThatSmart Jun 7, 2024