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25 December, 18:40

A standard deck of cards contains 52 cards. The cards have 4 different suits: clubs, diamonds, hearts, and spades. For each suit, there are 13 cards: one for each of the values 2 through 10, jack (J), queen (Q), king (K), and ace (A). A poker hand consists of 5 cards chosen at random from a standard deck. a. How many poker hands have two or more aces? b. How many poker hands contain the king of diamonds, the queen of hearts, or both?

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  1. 25 December, 21:10
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    a. 108336, b. 480200

    Step-by-step explanation:

    a. No. of ace cards = 4

    No. of non ace cards = 48

    We draw 5 cards

    So,

    No. of ways of 2 aces = C (4,2) C (48,3)

    No. of ways of 3 aces = C (4,3) C (48,2)

    No. of ways of 4 aces = C (4,4) C (48,1)

    Hence

    No. of ways of 2 or more aces

    = C (4,2) + C (48,3) + C (48,3) + C (4,3) C (48,2) + C (4,4) C (48,1)

    = 6 (17296) + 4 (1128) + (48)

    = 108336

    b. No of ways any 5 cards can be chosen = C (52,5)

    No. of ways kings of diamonds or queen of hearts is chosen = C (50,5)

    Hence

    No. of ways of choosing king of diamonds, queen of hearts or both = C (52,5) - C (50,5)

    = 480200
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