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Math Help - Subsets

  1. #1
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    Subsets

    This is my question, i can do the first part but then i need help with the rest please.

    How many ordered 5-subsets of {0,...,9} are there? How many of these start with 0? How many positive integers of exactly 5 digits, but with no two digits the same, are there? (In base 10.)
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  2. #2
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    Re: Subsets

    Quote Originally Posted by jonnyl View Post
    How many ordered 5-subsets of {0,...,9} are there? How many of these start with 0? How many positive integers of exactly 5 digits, but with no two digits the same, are there? (In base 10.)
    These are permutations: _NP_k=\frac{N!}{(N-k)!}
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    Re: Subsets

    So how would i use this to do the rest of the question?
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    Re: Subsets

    Quote Originally Posted by jonnyl View Post
    So how would i use this to do the rest of the question?
    You should show some effort here.
    What answer do you get for the first part?
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  5. #5
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    Re: Subsets

    I got 30240 for the first part, then 3024 for the second. But i dont really know how to do the last bit
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  6. #6
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    Re: Subsets

    Quote Originally Posted by jonnyl View Post
    I got 30240 for the first part, then 3024 for the second. But i dont really know how to do the last bit
    Those are correct.
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  7. #7
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    Re: Subsets

    so how would i go about doing the last part?
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  8. #8
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    Re: Subsets

    Quote Originally Posted by jonnyl View Post
    so how would i go about doing the last part?
    It depends on how one understands the question.
    We all know that 70412 is a five digit number with all digits different.
    But would 09876 also count? It is five digits all of which are different.
    If we do not allow a leading zero then the answer is:
    _{10}P_5 -~_9P_4.
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  9. #9
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    Re: Subsets

    But surely _{10}P_5-~_9P_4 is inclusive of numbers with repeated digits?
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  10. #10
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    Re: Subsets

    Quote Originally Posted by jonnyl View Post
    But surely _{10}P_5-~_9P_4 is inclusive of numbers with repeated digits?
    No, it most certainly does not.
    If you do that calculation, you will see the result is just the answer in part 1 minus the answer in part 2.
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