A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards for each suit (one for each rank). How many different hands of 7 cards…
a. contain 4 cards of one rank and 3 cards of a second rank?
b. contain 3 pairs of 3 different ranks and a single card of a fourth rank?
My attempt
a)$P(13,2)*C(4,4)*C(4,3)$ ways
b) $C(13,3),C(4,2),C(4,2),C(40,1)$