In a standard deck of $52$ cards, there are $4$ suits: clubs, diamonds, hearts and spades. For each suit, there are $13$ numbers ranging from A (Ace), 2, 3, ..., 10, J (Jack), Q (Queen), K (King). In the game Bridge, each player gets $13$ cards from a standard deck of $52$ cards. How many sets of $13$ cards are there where
a. all $13$ cards have the same suit?
b. the $4$ aces are part of the $13$ cards?
c. none of the $13$ cards have the same number?
d. exactly seven of the $13$ cards are spades?
e. at least seven of the $13$ cards are spades?
I think I understand A, $C(52,13) \cdot 4$, and B would be $C(4,4) + C(48,9) + C(47,8) \ldots + C(40,1)$. I feel like C would be similar to A but I'm not sure how, and for D and E I am completely lost, I don't know when I should multiply combinations and when I should use permutations.