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?
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
Less than 1.5 mins.