Ok, so I have a test tomorrow and there are a few problems that still don't make sense to me, any help on any one of these would be appreciated.

1) How many sequences of length 5 can be formed using the digits 0 through 9 with the property that exactly 2 of the 10 digits appear (e.g. 05550).

For this one, I get 10 * 9 * C(5,2). But the book tells me I'm wrong and I don't understand why.

2) How many five-card hands are there such that either all cards are from the same suit or from exactly two different suits?

I think it starts with C(13,2). Then choose a way to choose from exactly two suits, this part doesn't make sense to me