Selecting Teachers

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odod: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Tue Jan 13, 2009 12:59 pm; Location: Toronto; Thanked: 1 times

by odod » Tue May 12, 2009 11:43 am

Hello,

I found this question on a site that is advertising their GMAT product. It gave a test of a few sample questions and I can't figure this one out. Here is the question and answer (see spoiler). Please help!

If 3 teachers are to be selected from a group of 3 English Teachers, 2 Math Teachers and 4 History Teachers, what is the probabilty that 2 of the 3 selected are English Teachers?

[spoiler]Answer - 1/56[/spoiler]

ODOD

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Source: Beat The GMAT — Problem Solving | Tue May 12, 2009 11:43 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: Selecting Teachers

by Vemuri » Wed May 13, 2009 3:15 am

Let English Teacher be represented as E
Let Math Teacher be represented as M
Let History Teacher be represented as H

Out of the 3 teachers, 2 should be English Teachers. The various possibilities are:

EEM --> this can be arranged in 3 ways
EEH --> this can be arranged in 3 ways

So, the probability = 6/(9c3) ==> 6/84 ==> 1/14

Am I missing something?

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avenus: Master | Next Rank: 500 Posts; Posts: 238; Joined: Tue Feb 10, 2009 8:44 am; Thanked: 9 times

Re: Selecting Teachers

by avenus » Wed May 13, 2009 3:44 am

Vemuri wrote:Let English Teacher be represented as E
Let Math Teacher be represented as M
Let History Teacher be represented as H

Out of the 3 teachers, 2 should be English Teachers. The various possibilities are:

EEM --> this can be arranged in 3 ways
EEH --> this can be arranged in 3 ways

So, the probability = 6/(9c3) ==> 6/84 ==> 1/14

Am I missing something?

EEM --> this can be arranged in 3*2 ways (2 math teachers)
EEH --> this can be arranged in 3*4 ways (4 history teachers)

So my answer is 3/14

Last edited by avenus on Wed May 13, 2009 5:01 pm, edited 1 time in total.

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scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Wed May 13, 2009 3:57 am

am getting 3/14 too, but its nowhere close to the OA given

2 out of 3 english teachers can be selected in 3C2 ways.
1 teacher out of 6 non english teachers can be selected in 6C1 ways.

probabilty of selecting a team of 3=3C2*6C1/9C3=18/84=3/14 ways.

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