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January 30, 2015

January 30, 2015

Posted by **Jake** on Thursday, May 24, 2012 at 12:18am.

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 -
**MathMate**, Thursday, May 24, 2012 at 7:11am12 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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