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How many ways are there to put 4 distinguishable balls into 3 indistinguishable boxes?

 Jun 27, 2021
 #1
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Because the box is indistinguishable, we can use the reccurence relation. \(B(n,k)=B(n−1,k−1)+kB(n−1,k)\)with \(B(n,1)=1B(n,1)=1\) and \(B(n,n)=1B(n,n)=1\). For your case, you need the sum \(B(4,1)+B(4,2)+B(4,3)\). I trust you can use the formula to complete the problem.

 Jun 27, 2021
 #2
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HINT: There are 4 balls and 3 boxes, where all the balls are different. One of the 3 boxes has to have 2 balls.

 Jun 29, 2021

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