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# Distinguishability is Annoying

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How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are?

Greatly appreciated, MathE

Oct 21, 2018

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$$n \text{ identical objects can be placed into }r \text{ distinguishable boxes in }\\ N=\dbinom{n+r-1}{r-1} \text{ ways}\\ \text{In this problem }n=4,~r=3\\ N=\dbinom{6}{2}=15 \text{ ways}$$

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Oct 21, 2018

$$n \text{ identical objects can be placed into }r \text{ distinguishable boxes in }\\ N=\dbinom{n+r-1}{r-1} \text{ ways}\\ \text{In this problem }n=4,~r=3\\ N=\dbinom{6}{2}=15 \text{ ways}$$