I have a quiz tomorrow in an elementary combinatorics class, and I'm trying to understanding these generating function problems. For some reason, I can't see to figure out how to set these two up. Also, when the problem asks "find the number of ways" I just have to find the generating function and then what terms' coefficient I'm interested is - not the actual coefficient itself.
Problem 1: Find the number of ways to select 10 balls from a bin containing 10 balls each of 5 different colors.
Maybe I'm just stupid, but I was having trouble interpreting this question - what is meant by "10 balls each of 5 different colors" ? Wouldn't that mean I have 50 balls, not 10 in the bin, or does it mean that each of the 10 balls could be any of 5 different colors (and if this is the case, I have no idea where to start). I just don't get what it's asking … (maybe I should have posted this in an English forum).
Problem 2: Now, find the number of ways to selected 10 balls when there are 10 balls of one color, but only 8 balls of the other 4 colors.
Here, again, I am shaky on the interpretation. Are there 8 of each remaining color (i.e. 32 balls with 8 of each of the 4 colors) - or are there are 8 balls along the total of 4 colors - and how would you set that up
All the other problems on the practice sheet were really straightforward, so I feel like there isn't anything tricky here - but I don't see how to start.