[Combinations and Permutations] [Case Enumeration]

How many ways can you choose from a full deck (52 cards)
a) 4 cards of different suits and ranks?

b) 6 cards such that all four suits are represented among them?

#
a) A card of the spades suit can be chosen in 13 ways, after which a card of the diamonds suit can be chosen in 12 ways...

b) $6=1+1+1+3=1+1+2+2$.

## Answer

a) $13 \cdot 12 \cdot 11 \cdot 10=17160$ ways; b) $4 C_{13}^{3} \cdot 13^{3}+C_{4}^{2} \cdot 13^{2} \cdot\left(C_{13}^{2}\right)^{2}=8682544$ ways.