In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or german. If the group

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Wed Mar 03, 2021 10:45 am

GMAT Prep

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 Frech, how many different committees can be chosen?

A. 40
B. 50
C. 64
D. 80
E. 100

OA E

Solution:

Without any restrictions, the number of ways to choose 3 people from 10 is 10C3 = (10 x 9 x 8) / (3 x 2) = 720/6 = 120. Let’s assume a committee can be picked without any member who teaches French; then there are 6C3 = (6 x 5 x 4) / (3 x 2) = 120/6 = 20 ways. So there are a total of 120 different committees (if there are no restrictions) and 20 of them consist of no members who can teach French. Therefore, there must be 120 - 20 = 100 different committees with at least one member who teaches French.

Answer: E