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How to count

 

(a) Find the number of ways that Magnus can give out 20 identical stickers to 5 of his friends.  (Not everyone has to get a sticker.)

 

(b) Find the number of ways that Magnus can give out 20 identical stickers to 5 of his friends, if every friend gets at least one sticker.

 Jan 30, 2023
 #1
avatar+2667 
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a) There are 20 stars and 4 bars, so there are \({20 + 4 \choose 4} = \color{brown}\boxed{10,626}\) ways to give out the stickers

 Jan 30, 2023
 #2
avatar+2667 
+1

b) Start by giving each kid a sticker. Now, there are 15 stars and 4 bars for \({15 + 4 \choose 4} = \color{brown}\boxed{3,876}\) cases

 Jan 30, 2023

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