Probability of 5 cards drawn from shuffled deck 
Five cards are drawn from a shuffled deck with $52$ cards. Find the probability that
a) four cards are aces
b) four cards are aces and the other is a king
c) three cards are tens and two are jacks
d) at least one card is an ace

My attempt:
a) $\left(13*12*\binom{4}{4}*\binom{4}{1}\right)/\binom{52}{5}$
b) same as (a)?
c) $\left(13 * 12 * \binom{4}{3} * \binom{4}{2}\right)/\binom{52}{5}$
d) $\left(13 * \binom{4}{1}\right)/\binom{52}{5}$

deepsea gave a complete and clear answer.  
I'd just add that you could see straight away that the answers for (b) and (a) cannot be the same, because the requirement in (b) is so much more specific.  Many hands that satisfy (a) do not satisfy the conditions for (b).
