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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.)

 Jun 7, 2024
 #1
avatar+1280 
+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! :)

 Jun 7, 2024

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