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Math Help - How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

  1. #1
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    How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    How many EVEN 7 digit inters there using only the digits 2,3,4,5,6,7,8? EDIT: forgot to add the word even.

    I thought this was easy, but when I got my assignment back it was wrong.

    For my answer I put 4*6!

    4 ways to put either 2,4,6,8 in the last position multiplied by 6! as the ways we can arrange the rest of the numbers.

    If this is incorrect.....what am i missing?


    edit: I also got zero on a similar question.

    In a class of 19 children, with 11 boys and 8 girls - how many ways can we choose a team of 10 children containing at least 5 boys?

    I put...

    (11c5) to select the boys. Multiplied by (14c5) to select the rest of the 5 students.

    The correct solution apparently is (11c5)(8c5)+(11c6)(8c4)+(11c7)(8c3)+(11c8)(8c2)+(1 1c9)(8c1)+(11c10)(8c0)
    Last edited by ehpoc; December 14th 2011 at 12:24 PM.
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  2. #2
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    Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    Quote Originally Posted by ehpoc View Post
    How many 7 digit inters there using only the digits 2,3,4,5,6,7,8?
    I thought this was easy, but when I got my assignment back it was wrong.
    For my answer I put 4*6!
    4 ways to put either 2,4,6,8 in the last position multiplied by 6! as the ways we can arrange the rest of the numbers. If this is incorrect.....what am i missing?
    2,323,265 is a seven digit integer using only those seven digits.
    The question did not say that digits could be repeated. Did it?
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    Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    So in this case it would be 4*7^6?
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    Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    Quote Originally Posted by ehpoc View Post
    So in this case it would be 4*7^6?
    The question you posted said nothing about the number being even.
    Did you leave that out? If not why are you using that 4?
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  5. #5
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    Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    Yes so sorry! I left out the word even.

    So my rational is that there are 4 unique evens to select from multiplied by 7^6 for the other six numbers.

    Correct?
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    Re: How many 7 digit inters there using only the digits 2,3,4,5,6,7,8

    Quote Originally Posted by ehpoc View Post
    Yes so sorry! I left out the word even.
    So my rational is that there are 4 unique evens to select from multiplied by 7^6 for the other six numbers. Correct?
    In the future please review your postings.
    Yes it is correct.
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