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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.)

 Apr 2, 2024
 #1
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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.

 Apr 2, 2024

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