# Combinations - need help clarifying answers

I have the answers to the following two questions, but I'm stumped as to why the answers are calculated this way:

Q.1) There are six comics: A, B, C, D, E, F; How many ways are there to select six comics? Answer: C(6+6-1, 6-1)

Q.2) There are 20 balls. 6 red, 6 green, 8 purple. In how many ways can we select five balls if balls of the same color are considered identical? Answer: C(3+5-1, 5)

What I don't understand is why we subtract 1 from 6 in the first question while leaving 5 just the way it is in the 2nd question.

Any help would be appreciated. Thanks!

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Notice that $C(6+6-1,6-1)=C(6+6-1,6)$, so it doesn't matter whether you subtract 1 from the 6 or not.
In the second problem, $C(3+5-1,5)=C(3+5-1,3-1)$, so you are in fact subtracting 1 --- it's just that you're subtracting it from the 3 (the number of different kinds of item), not from the 5 (the number of items chosen). This is the same as the first problem, where you either subtract 1 from the number of different kinds of item, 6, or don't subtract it from the number of items chosen, which is also 6.