How many ways are there to put 2 white balls and 2 black balls into 3 boxes, given that balls of the same color are indistinguishable, but the boxes are disti nguishable?

Work:

Put first the P white balls into the N different boxes which can be done in (P+N−1,P)

,then for each of these you do the same with the black balls so overall the answer is (P+N−1,P)(Q+N−1,Q) so the answer should be (5,2)*(5,2)

(5, 2) = 5!/(3!*2!) = 10

10*10 = 100

Please help check. Thank you

DragonLord Mar 24, 2020

edited by
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Mar 24, 2020