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In a certain group of 10 members, 4 members teach only

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In a certain group of 10 members, 4 members teach only [#permalink] New post 13 Feb 2007, 09:59
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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

I was stumped with this one. Please explain you answer?!
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Re: PS - GMATPrep - 3 member committee [#permalink] New post 13 Feb 2007, 10:42
jylo 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

I was stumped with this one. Please explain you answer?!


There cases:

case 1: 1 french teacher
4C1* 6C2 = 60

case 2: 2 french teacher
4C2* 6C1 = 36

case 3: 3 french teacher
4C3 = 4

Answer: 100
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Re: PS - GMATPrep - 3 member committee   [#permalink] 13 Feb 2007, 10:42
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