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Math Help - Number of Choices..

  1. #1
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    Question Number of Choices..

    Hi all,

    Please help me on this..

    Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
    a) Exactly 3 consonants
    b) No vowels
    c) At least one vowel
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by cu4mail View Post
    Hi all,

    Please help me on this..

    Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
    a) Exactly 3 consonants
    b) No vowels
    c) At least one vowel
    {10}\choose{5}
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  3. #3
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    Thanks

    Quote Originally Posted by colby2152 View Post
    {10}\choose{5}
    Thanks for help.
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  4. #4
    Super Member angel.white's Avatar
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    Quote Originally Posted by cu4mail View Post
    Hi all,

    Please help me on this..

    Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
    a) Exactly 3 consonants
    b) No vowels
    c) At least one vowel
    I think I can answer, if anyone wants to check my work I wouldn't mind

    a) 3 of your letters are used up by choosing vowels. So you have 2 choices left out of 7: (10-3)C(5-3) = 7C2 = 21

    b) You still need to select 5 letters, but your set is smaller (10-3)C5 = 7C5 = 21

    c) This should be the set of all choices minus the set of no vowels. 10C5 - 7C5 = 252 - 21 = 231


    I am moderately confident in my answers, but I haven't looked at these in a while, so take it with skepticism.

    edit: I think I did a wrong, I calculated how many vowels instead of how many consonants.
    Last edited by angel.white; January 27th 2008 at 12:23 AM.
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