A deck of 52 cards is mixed well, and 5 cards are dealt.
a. It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible five-card hands, of which only 1287 are hands consisting entirely of spades. What is the probability that a hand will consist entirely of spades? What is the probability that a hand will consist entirely of a single suit?
b. It can be shown that exactly 63,206 hands contain only spades and clubs, with both suits represented. What is the probability that a hand consists entirely of spades and clubs with both suits represented?
c. Using the result of Part (b), what is the probability that a hand contains cards from exactly two suits?