1. Combination

Hello,
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?

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?

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!

2. Re: Combination Originally Posted by pauliwago Hello,
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?
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?
$\displaystyle \binom{N+k-1}{N}$ ways to select $\displaystyle N$ items from $\displaystyle k$ different types.
$\displaystyle \binom{12+20-1}{12}$.
combination 