# Math Help - Combination

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?

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!
These are also known as multi-selections.
$\binom{N+k-1}{N}$ ways to select $N$ items from $k$ different types.

There twenty kinds s of doughnuts, how many ways can we select a dozen :
$\binom{12+20-1}{12}$.