kimmyg wrote:

In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committees can be chosen?

(A) 40

(B) 50

(C) 64

(D) 80

(E) 100

Please explain

Easiest and shortest way to solve a combination with a constraint is to

First Find the Total Combination w/o constraints

10 C 3 = 120

Find the Combination of NO French teachers 6 C 3 = 20

Subtract the the Combination of having no French teachers from the total

10C3-6C3=100

Less than 1.5 mins.