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