In a certain group of 10 members, 4 members teach only French and the rest teach only German or Spanish. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen?
a) 40
b) 50
c) 64
d) 80
e) 100
Please suggest how to solve the problem. The OA is e.
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E (Group is of total 3 teachers)
1. When 1 French teacher & 2 german / spanish = 4C1 * 6C2 = 60
2. When 2 French teacher & 1 german / spanish = 4C2 * 6C1 = 36
3. When 3 French teacher & 0 german / spanish = 4C3 * 6C0 = 4
Total number of groups = 100
Thanks for the explanation PM.
Two ways to count combinations
The FAST Way is :
“At least 1…” combinations = Total Possible Combinations – “0…” combinations
Total = 3C10 = 10!/(7!3!) = 120
“0…”= 0C4*3C6 = 3C6 = 6!/(3!3!) = 20
Hence “At least 1…” = 120-20 = 100
So correct answer is E
The LONG way is PM’s offered solution.