In a certain group of 10 members,4 teach only french and rest teach spanish or german.if the group is to chose 3 member comittee which must have atleast 1 member who teaches french,how many diff commitess can be chosen?
ans = 100
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Frankenstein
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Hi,
From a group of 10 members, 3 members can be chosen in 10C3 = 120 ways
The committee can be formed without any French teachers in 6C3 ways = 20 ways
So, number of committees with at least 1 French teacher = 120-20 = 100
From a group of 10 members, 3 members can be chosen in 10C3 = 120 ways
The committee can be formed without any French teachers in 6C3 ways = 20 ways
So, number of committees with at least 1 French teacher = 120-20 = 100
Cheers!
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winniethepooh
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Another way to solve this can be the probability of there being only 1 french teacher and 2 other teachers + 2 french teachers and 1 other teacher + 3 french teachers and none of the other teachers.
= 4C1 x 6C2 + 4C2 x 6C1 + 4C3 x 6C0
= 4 x 15 + 6 x 6 + 4 x 1
= 60 + 36 + 4
= 100
= 4C1 x 6C2 + 4C2 x 6C1 + 4C3 x 6C0
= 4 x 15 + 6 x 6 + 4 x 1
= 60 + 36 + 4
= 100
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winniethepooh
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