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!