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If you are dealt 55 cards from a shuffled deck of 52 cards, find the probability of getting threethree queensqueens and twotwo kingskings.

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  1. 18 May, 21:10
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    We need to find the probability of getting 3 queens and 2 kings

    In 52 cards, we have 4 queens and 4 kings

    We need to select 3 queens from 4 queens

    /[/frac{n!}{r! (n-r) !}/]

    So different combinations of selecting 3 queens from 4 queens is 4C3

    /[/frac{4!}{3! (4-3) !}/] = 4

    We need to select 2 kings from 4 kings

    /[/frac{n!}{r! (n-r) !}/]

    So different combinations of selecting 2 kings from 4 kings is 4C2

    /[/frac{4!}{2! (4-2) !}/] = 6

    Total combination of selecting 5 cards from 52 cards = 52C5

    /[/frac{52!}{5! (52-5) !}/] = 2598960

    Probability of getting 3 queens and 2 kings = 4C3 * 4C2 / 5C52

    /[/frac{4*6}{2598960}/]

    1 / 108290
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