I am having real trouble figuring out when to use these two formulas:

c(k + t - 1, t-1) and c(k + t - 1, k)

where k is equal to number of selections

t is equal to number of elements; number of groups items are in I guess is another way to state that

For example:

There are piles of red, green and blue balls; each pile has at least 10 balls in it. How many ways can you select 10 balls?

I would think it would be c(10 + 3 - 1, 3-1) but the answer the book gives is c(10 + 3 - 1, 10)

Another one is:

How many ways can 10 be selected if exactly one red ball must be selected?

I get c(9 + 2 - 1, 2-1) but again the answer is c(10 +2 -1, 9)

Please help this confused person!!!!

You have a bag with twenty balls in it. six red six green and 8 purple

How many ways can we select 5 balls if balls of each specific color are identical?

i think this is 20!

______

6!6!8!

Could you tell me if this is correct? Thanks again folks very much.