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How many ways can you distribute 4 identical balls among 4 different boxes?

 Sep 25, 2020
 #1
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+2

Ok, so here is my version of the answer to this problem.

 

We can determine that we can split the balls into the groups 4-0-0-0, 3-1-0-0, 2-2-0-0, 2-1-1-0, and 1-1-1-1. Now we have to count how many ways the boxes can be chosen.

For 4-0-0-0, there are 4 ways we can choose the box that gets all four balls.

For 3-1-0-0, there are 4 ways we can choose the box that gets three balls, then 3 ways we can choose the box that gets one ball.

For 2-2-0-0, there are \(\binom{4}{2} = 6\) ways we can choose the two boxes that get two balls each.

For 2-1-1-0, there are 4 ways we can choose the box that gets two balls, then 3 ways we can choose the box that gets no balls (then the other two boxes get one ball each).

For 1-1-1-1, there is only one way.

The total number of ways is then \(4 + 4 \cdot 3 + 6 + 4 \cdot 3 + 1 = \boxed{35}.\)

 

Hope this helped! angel

 Sep 25, 2020
 #2
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0

Thank you! That's correct!

Guest Sep 25, 2020
 #3
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+1

Glad to help!

ETERNITY  Sep 25, 2020

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