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There are 10 language professors, 4 of them teach only frenc

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There are 10 language professors, 4 of them teach only frenc [#permalink] New post 27 Aug 2009, 06:36
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There are 10 language professors, 4 of them teach only french, the rest teach only spanish or german. How many groups of 3 teachers with at least 1 french teacher can be formed?
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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 27 Aug 2009, 06:47
Number of ways of selecting the group of 3 with atleast one French teacher =
= 6c2*4c1 + 6c1*4c2 + 6c0*4c3
= 60 +36 + 4 = 100
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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 28 Aug 2009, 04:23
Agree with Aleehsgonji (i nearly broke my finger typing you nickname ;))))) Just want to add a little bit of explanation.

The possible arrangements are:

1) One F AND two S/G, OR
2) Two F AND one S/G, OR
3) Three F

1) We choose one French professor out of four French professors AND (which means that we should multiply the number of ways in which we can arrange french and spanish/german professors) we choose two S/G professors out of six S/G professors (10 - 4 French = 6 S/G). Translating into mathematical symbols, we get: 1C4*2C6
2) Similarly, we construct the equation for possible arrangement 2): 2C4*1C6
3) 3C4

Since either of the arrangements is possible (see OR, which means that we should sum all the arrangements), the final equation looks like:
1C4*2C6+2C4*1C6+3C4

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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 28 Aug 2009, 04:56
atleast one french prof means (1F+2S/G) OR (2F+1S/G) OR (3F)
4C1*6C2 + 4C2*6C1 + 4C3 = 100
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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 29 Aug 2009, 05:47
Atleast 1 french means = total - no french
= 10C3 - 6C3
= 120 - 20 = 100
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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 29 Aug 2009, 08:23
gmate2010 wrote:
Atleast 1 french means = total - no french
= 10C3 - 6C3
= 120 - 20 = 100


yep, this one is quicker.
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Re: There are 10 language professors, 4 of them teach only frenc [#permalink] New post 31 Aug 2009, 13:30
You are right.
Oa is 100
Re: There are 10 language professors, 4 of them teach only frenc   [#permalink] 31 Aug 2009, 13:30
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There are 10 language professors, 4 of them teach only frenc

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