Probability of Poker Hands

Hello and thank you in advance for any help you may be able to give me!

I am stuck on the following question:

A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards.

a) How many poker hands are possible?

b) How many different hands consisting of 3 kings and 2 queens are possible? c) A full house consists of 3 cards of one denomination and 2 cards of another. How many different full houses are possible?

d) Calculate the probability of being dealt a full house.

On "a" I am stuck on 2 different answers. My first answer I figured c1*c1-1*c1-2*c1-3*c1-4= 52*51*50*49*48= 311,875,200 because I figured every time you dealt a card, there was one less card to be dealt in the deck. However, looking around different sites I keep seeing that the answer to part "a" is c(52,5) = 2,598,960. So now I don't know which is correct.

As for parts b-d I'm completely lost!

Thanks again for any help!!!