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Recall that in a standard set of playing cards, there are 4 suits, {*, ,, and 13 ranks LA 2, 3, 4,5, 6, 7, 8.9, 10. J Q. K . There is a card for every (rank.suit) combination. A hand of cards is another word for set. A 5-card hand of cards is a set of cards with 5 elements. Poker is a game that is often played with 5-card hands. (For cach problem, your answer should be left in factorials, exponentials, or binomial coefficients. Give a brief justification of how you got your answer.) (f) How many ways can you deal (give) five people each a 2-card hand from a deck of 52 cards if at least one person has an A? (g) Suppose you have a deck with only the 13 diamonds: (A◇,20,30, 4◇,50,60,7◇ 80,90,10 , J◇, Q◇, K◇ . How many ways can you distribute the diamonds to 3 friends (Alice, Bob and Charlie) such that each friend has at least one card? (order within the pile does not matter.)

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