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18 November, 17:08

Jimmy found five numbered cards, 1, 2, 3, 4, and 5 under his brother's bed. In how many ways can he arrange the cards to form a five-digit number?

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  1. 18 November, 17:15
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    120 ways

    Step-by-step explanation:

    Given.

    Cards numbered 1 - 5

    Required

    Number of arrangements

    First, it should be noted that there's no way Jimmy can repeat cards because the each card contains distinct numbers.

    Having said that;

    Number of cards = 5

    Required digit = 5-digit

    This question will be solved using permutation formula.

    nPr = n! / (n - r) !

    Where

    n = number of cards = 5

    r = number of digits = 5

    So,

    nPr = n! / (n - r) ! becomes

    5P5 = 5! / (5 - 5) !

    5P5 = 5!/0!

    5P5 = 5!/1

    5P5 = 5!

    5P5 = 5 * 4 * 3 * 2 * 1

    5P5 = 120 ways.

    Hence, number of possible arrangements Jimmy can arrange the card is 120 ways.
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