statistics permutations and combinations
posted by Celee .
Selecting a committee: There are 7 women and 5 men in a department. How many ways can a committee of 4 be selected if there must be at least 2 women?

3 cases :
2 women, 2 men > C(7,2)xC(5,2) = 21(10) = 210
3 women, 1 man > C(7,3)xC(5,1) = 35(5) = 175
4 women, 0 men > C(7,4) = 35
add up the 4 cases to get 420
or, exclude the case of no women, and one woman
C(12,4)  C(7,1)xC(5,3)  C(7,0)x(C5,4)
= 495  70  5 = 420