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How many ways can you distribute 4 identical balls among \(5\) identical boxes?

 Jan 31, 2022
 #1
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Because both the balls and the boxes are indistingusable, we only have to account for each case once.

 

Here are the only possibilites: 

 

\(4\) in one basket and \(0\) in the rest.

\(3\) in one basket and \(1\) in \(1\) of the remaining \(4\) baskets, with none in the rest

\(2\) in one basket and \(2\) in another basket, with none in the rest

\(2\) in one basket and \(1\) in another and \(1\) more in another basket, with none in the rest

\(1\) in one basket and \(3\) in another, with none in the rest.

 

This accounts for a total of \(\color{brown}\boxed5\) ways.

 Jan 31, 2022

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