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(a) How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable and the boxes are distinguishable?

(b) How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?

(c) How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

(d) How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?

(e) How many ways are there to put 6 balls in 3 boxes if three balls are indistinguishably white, three are indistinguishably black, and the boxes are distinguishable?

Oct 25, 2017

#1
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Hi Mr O

I answered a question very simiar to this a day or two ago. I seem to recall you left a comment too..

Anyway, I'd like to see you attempt these questions, one at a time if you want, and then maybe we can talk about your answer/s.

Why don't you start with b, that looks like the easiest one because the only thing that matters is how many balls are in the boxes.

Oct 25, 2017