# Distributing ten $1 coins to 6 employees Permutations and combinations completely melt my brain so I hope someone could verify I'm correct here: I want to distribute ten$1 coins to six employees so that no employee gets more than 2 dollars. It's also possible some employees get nothing.

As far as I can tell there are 2 possible distribution methods:

2 2 2 2 2 0

and

2 2 2 2 1 1

So that should be C(6,1) + C(6,2) = 21

Is that correct, or am I missing something?

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I presume you find these 2 cases by hand. It is better to think this problem with generating functions so you take out the "find all possibility" part of the step. I'm saying this because this late into a semester and if you still haven't seen GF yet, you might never go into GF in your course, but it would be something nice to know. – Chao Xu Nov 22 '12 at 20:44