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Math Help - Permutations

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    Permutations

    To cancel an electronic alarm, a 5-digit code number must be entered into the code box. Assuming that digits may be repeated, how many codes are possible?
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  2. #2
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    Quote Originally Posted by Joker37 View Post
    To cancel an electronic alarm, a 5-digit code number must be entered into the code box. Assuming that digits may be repeated, how many codes are possible?
    There are ten digits: 0, 1, 2,...8, 9
    Think of this question from perspective of the person who sets the code.

    When he picks the first of the 5 digits, how many choices does he have? Exactly 10 choices!

    When he picks the second of his 5 digits, he can again choose from 10 options.

    For digits 3, 4 and 5 he also has 10 choices.

    So he has 10*10*10*10*10 choices or 10^5.

    To contract: if repetition is not allowed, there are
    10*9*8*7*6 choices.
    For the first digit he can choose any number 0-9.
    For the second digit he can choose any number 0-9 EXCEPT the number he chose for the first digit, so he has 9 options.
    And so on.
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