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A total of 10 teachers. 4 teach French, others teach Spanish

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A total of 10 teachers. 4 teach French, others teach Spanish [#permalink] New post 07 Jun 2004, 22:27
A total of 10 teachers. 4 teach French, others teach Spanish and German. Form a committee of 3 teachers, with at least one French techer in the commitee.

OA is 100
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 [#permalink] New post 07 Jun 2004, 23:00
From what I see,correct answer is 72.

one french can be selected in 4C1=4 ways.
For the two remainig slots, no restrictions, just need to pick 2 from 9 people.9C2=36
ans = 36*4/2!=72 (this is committe, order is not important)
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 [#permalink] New post 07 Jun 2004, 23:34
I am not that confident with my solution. Anybody comments? i need to look at the concepts again I guess. May be, I am spending too much time at the forum than preparing from the books.
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 [#permalink] New post 08 Jun 2004, 00:43
There are 3 cases here: -

You can select: -

1. One French, One Spanish and One German in 4C1(French) X 6C2 (S + G) = 4 X 15 = 60

2. Two French and one Spanish or one German in 6C1 ( S / G) X 4C2 (F)

= 36
3. All the 3 french in 4C3 ways = 4

60+36+4 = 100

Alternately: -

You can select any 3 from the 10 in 10C3 ways ---------(1)

You can select persons other than French in 6C3 ways-------(2)

So the number of ways in which at least a french will be included in the committee is 10C3-6C3 = 120 - 20 = 100 ways
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 [#permalink] New post 08 Jun 2004, 02:56
Hi Mayur

Fantastic. I understood the 1st approach clearly. Thanks man.

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  [#permalink] 08 Jun 2004, 02:56
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A total of 10 teachers. 4 teach French, others teach Spanish

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