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Math Help - Work Woes

  1. #1
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    Exclamation Work Woes

    The executive director of the "smart solutions" company wishes to employ 9 new staff members. There are 14 applicants: 4 Mathemiticians and 10 accountants. In how many ways can the executive director select 9 people if he wants to employ atleast one mathematician?

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  2. #2
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    Quote Originally Posted by googa View Post
    The executive director of the "smart solutions" company wishes to employ 9 new staff members. There are 14 applicants: 4 Mathemiticians and 10 accountants. In how many ways can the executive director select 9 people if he wants to employ atleast one mathematician?

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    At least one Mathematician.

    4M and 5A
    3M and 6A
    2M and 7A
    1M and 8A
    -------------------
    4 ways ---------------answer.
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  3. #3
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    Hello, googa!

    The executive director of a company wishes to employ 9 new staff members.
    There are 14 applicants: 4 Mathematicians and 10 Accountants.
    In how many ways can the executive director select 9 people
    if he wants to hire at least one Mathematician?
    There are: . {14\choose9} = 2002 possible selections.


    The opposite of "at least one Mathematician" is "no Mathematicians" (all Accountants).

    There are: . {10\choose9} = 10 ways to choose all Accountants (no Mathematicians).


    Therefore, there are: . 2002 - 10 \:=\:\boxed{1992} ways that have at least one Mathematician.

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