math
posted by Jake .
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?

12 men and 8 women.
Define:
(n,r)=n choose r = n!/((nr)!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.