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Twenty people apply for seven jobs that are available at fly by night aircraft company

12 are men and the rest are women.

How many seven person groups have exactly three men?
How many of these seven person groups have exactly three men or three women?

  • math -

    12 men and 8 women.

    Define:
    (n,r)=n choose r = n!/((n-r)!r!)
    Example: (5,3)=5!/(2!3!)=5*4/2!=10


    A. exactly 3 men and 4 women
    Choose the 3 men in (12,3) ways and the 4 women in (12,4) ways. The number of groups which has exactly 3 men is therefore (12,3)*(12,4)=220*495 ways.

    B. 3 men + 4 women or 3 women + 4 men
    Proceed as in A for 3 women + 4 men and add the result to that of A.

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