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Math Help - Permu

  1. #1
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    Permu

    let A be a set of 4 digit nos a1,a2,a3,a4 where a1>a2>a3>a4, then n(A) is equal to
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  2. #2
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    Red face Re: Permu

    This can be solved by using combination. Make this a function where X={a1,a2,a3,a4} and Y={0,1,2,...9}. All you have to do is pick 4 numbers from Y. You dont even need to think about the order because the biggest number automatically becomes a1 and the smallest number becomes a4.
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  3. #3
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    Re: Permu

    Hello, prasum!

    Very sloppy wording . . .


    \text{Let }A\text{ be a set of 4-digit numbers} composed of the digits \{a_1,a_2,a_3,a_4\}
    \text{ where }a_1>a_2>a_3>a_4, and each digit is used once.

    \text{ Find }n(A).

    * .The problem said that the 4-digit numbers are: . a_1, a_2, a_3, a_4.
    . . Therefore:. n(A) \,=\,4. . (duh!)

    * .If the digits can be repeated:. n(A) \:=\:4^4 \:=\:256.

    Having said all that:. n(A) \,=\,4!\,=\,\boxed{24}


    BTW the inequality was given to indicate that the digits are distinct.

    If the digits were \{2,7,7,9\} or \{3,3,3,8\}, the answers would "depend".

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  4. #4
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    Re: Permu

    Quote Originally Posted by prasum View Post
    let A be a set of 4 digit nos a1,a2,a3,a4 where a1>a2>a3>a4, then n(A) is equal to
    I think that reply #2 is correct.
    This question is about what is known as strictly sorted natural numbers with descending digits.
    Example: 7421 and not 7412.
    Any set of four distinct digits corresponds to a strictly sorted natural number with descending digits.
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