Consider a standard deck of playing cards (as described on page 242). (a) How many hands (sets) of…

Consider a standard deck of playing cards (as described on page 242).

(a) How many hands (sets) of 5 cards can be dealt from such a deck (which contains 52 distinct cards)?

(b) In poker, such a 5-card hand is called a full house if it contains two cards of one value and three of another (for example, two 5s and three 9s). How many 5-card hands are a full house?

(c) A much more common poker hand is two pair: two cards of one value, two cards of another value, and one card of a third value (for example two 5s, two 9s, and one K). How many 5-card hands are a two pair?

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