+1036 Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)
+394 Since it's not specified whether Magnus can have stickers left over:
This is the solution if you don't have to hand out every sticker.
a + b <= 12.
Create a dummy variable, k, for all leftovers
a + b + k = 12.
This is great because we see k has to be at least 0, like all the others.
Apply stars and bars formula:
\({12+3-1\choose 3-1}=91\).
There are 91 ways.
This is the solution id you don't have to hand out every sticker.
Give one friend any number of stickers 0 -12.
The other gets all the rest.
There are 13 ways.
