Count the number of different functions with the given domain, target and additional properties.

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This question refers to a standard deck of playing cards. If you are unfamiliar with playing cards, there is an explanation in Section 11.1 under the heading "Standard playing cards." A five-card hand is just a subset of 5 cards from a deck of 52 cards.

(d) How many five-card hands have four cards of the same rank?

(e) A "full house" is a five-card hand that has two cards of the same rank and three cards of the same rank. For example, {queen of hearts, queen of spades, 8 of diamonds, 8 of spades, 8 of clubs}. How many five-card hands contain a full house?

(f) How many five-card hands do not have any two cards of the same rank?

(c) f: (0,1) 10,1 (d) f: (0,1)5 (0,1)7. The function f is one-to-one