1) Cards are dealt, one at a time, from a standard 52 card deck.

a) if the first 2 cards are both spades, what is the probability that the next 3 are also spades?

2) 5 cards are drawn from a standard 52 card deck. What is the probability that all 5 cards will be from the same suit?

3) A gambler has been dealt 5 cards: 2 are aces, one is a king, one a 5 and one 9. He discards the 5 and 9 and is dealt 2 more cards. What is the probability that he ends up with a full house?

For 1) all I know is that it's a conditional probability, but I have no clue what values to take

For 2) is it $\displaystyle \frac{4}{2,598,960}$ since it's $\displaystyle \binom{52}{5}$ and there are 4 possible suits.

For 3) I'm stuck on the values that I have to pick. Is it $\displaystyle \binom{47}{2} = 1081$ for the denominator, and $\displaystyle \binom{2}{1} \ \binom{3}{1}$ for the numerator, which equals $\displaystyle \frac{6}{1081}$ ?