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(a) In how many ways can you distribute 4 distinguishable balls among 3 indistinguishable boxes?

 

(b) In how many ways can you distribute 4 indistinguishable balls among 5 distinguishable boxes?

 Dec 22, 2022
 #1
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(a)

This time we don't care about what balls are in what box, but the groupings of the balls a, b, c, and d. 

abcd (1 case)

abc, d (4 different cases)

ab, cd (4 choose 2 / 2 = 3 cases)

ab, c, d (4 choose 2 = 6 cases)

That's all: 1 + 4 + 3 + 6 = 14 total cases.

 Dec 22, 2022

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