This question refers to a standard deck of playing cards. If you are unfamiliar with playing cards, there is an explanation in "Probability of an event" section under the heading "Standard playing cards." A five-card hand is just a subset of 5 cards from a deck of 52 cards. (a) How many different five-card hands are there from a standard deck of 52 playing cards? (b) How many five-card hands have exactly two hearts? (c) How many five-card hands are made entirely of hearts and diamonds? (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?