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24 April, 11:31

Taking two cards, one by one, from a standard 52-card deck, how many different ways are there if (a). the first card is an ace and the second card is a king? (b). the first card is an ace and the second card is not a king? (c). the first card is a heart and the second card is an ace? (d). there is at least one ace in the two cards?

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  1. 24 April, 11:48
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    a) 16 ways

    b) 188 ways

    c) 39 ways

    d) 51 ways

    Step-by-step explanation:

    A standard deck of 52 cards consists of 4 suits of spades, hearts, diamonds and clubs. Each suit contains 13 cards. According to this:

    a)

    First card is an ace = 4 possible cards

    Second card is a king = 4 possible cards

    4 X 4 = 16 ways

    b)

    First card is an ace = 4 possible cards

    Second card is not a king = 51 cards - 4 kings = 47 possible cards

    4 X 47 = 188 ways

    c)

    First card is a heart = 13 possible cards

    Second card is an ace = 4 aces - 1 heart ace = 3 possible cards

    13 X 3 = 39 ways

    d)

    First card an ace = 1 card

    second card, any other card = 51 possible cards

    1 X 51 = 51 ways
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