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Math Help - General Counting Methods - combinatorics

  1. #1
    DBA
    DBA is offline
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    General Counting Methods - combinatorics

    Hello, I need help with this ...


    How many ways are there to pick first a vowel and then a consonant from MATHEMATICS?

    The answer is 15.

    I thought that I have
    4 vowels A E A I, thus 4 possible vowels
    and
    7 consonants M T H M T C S, thus 7 possible consonants

    Then 4*7=28 which is incorrect.

    How can I get to the answer 15?
    Thanks
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by DBA View Post
    Hello, I need help with this ...


    How many ways are there to pick first a vowel and then a consonant from MATHEMATICS?

    The answer is 15.

    I thought that I have
    4 vowels A E A I, thus 4 possible vowels
    and
    7 consonants M T H M T C S, thus 7 possible consonants

    Then 4*7=28 which is incorrect.

    How can I get to the answer 15?
    Thanks
    We treat the first A and second A as equivalent. Same with M and T. Thus we have 3 vowels and 5 consonants giving product 15.
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