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Math Help - digits

  1. #1
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    digits

    Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common fraction.
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  2. #2
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    Quote Originally Posted by sri340 View Post
    Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common fraction.
    Hi sri340,

    We can ask "how many have no repeated digits" ?

    This is 4! as all 4 digits must be different.

    There are 4^4 4-digit numbers given the digits may be repeated.

    Hence 4^4-4! contain at least one repeated digit.

    The fraction is \frac{4^4-4!}{4^4}=\frac{4(4^3-6)}{4(4^3)}=\frac{4^3-6}{4^3}
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