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Combinations -- CHALLENGE PROBLEM

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Combinations -- CHALLENGE PROBLEM

by Stockmoose16 » Wed Oct 22, 2008 1:18 pm
Company X has n regional offices, where n represents an even integer. Each regional office must recommend two candidates, one male and one female, to serve on the corporate auditing committee. If each of the offices must be represented by exactly one member on the auditing committee and if the committee must consist of an equal number of male and female employees, how many different committees can be formed?

Image

I tried to do the problem in the following manner, but I didn't get the correct answer:

Assume N=2

That means there are 4 choices: M1, M2, F1, F2

There are 2 positions available, and one must go to a male, one must go to a female.

So you can do the following:

M1F1
M1F2
M2F1
M2F2

That means there are four total possibilities if N=2. The OA is B. If you plug in 2 for N in that equation, you do not get 4. What am I missing here?
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by earth@work » Wed Oct 22, 2008 2:07 pm
is the OA .... B = n!/(.5n)!^2
Well, the way u took 2, i took n=10
If 1male & 1 female is recommended from 10 regional offices total will be 10 male +10 female i.e 10M+10F
committee will have only 1 representative from each office + no of males =no. of females
we need to pick 5 women out of 10 women + 5 men out of remaining 5 offices men i.e 5 out of 5 remaining men (we exclude those men who belong to same office as women already selected)
=10C5 *5C5 =(10!/5!*5!)*1 =10!/(5!)^2
now replacing 10 by n & 5 by n/2(=0.5n) we get =n!/(0.5n!)^2
do let me know if this is correct
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by Stockmoose16 » Wed Oct 22, 2008 2:31 pm
earth@work wrote:is the OA .... B = n!/(.5n)!^2
Well, the way u took 2, i took n=10
If 1male & 1 female is recommended from 10 regional offices total will be 10 male +10 female i.e 10M+10F
committee will have only 1 representative from each office + no of males =no. of females
we need to pick 5 women out of 10 women + 5 men out of remaining 5 offices men i.e 5 out of 5 remaining men (we exclude those men who belong to same office as women already selected)
=10C5 *5C5 =(10!/5!*5!)*1 =10!/(5!)^2
now replacing 10 by n & 5 by n/2(=0.5n) we get =n!/(0.5n!)^2
do let me know if this is correct
Yes, your answer is correct, but I was asking why my logic isn't working?
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Re: Combinations -- CHALLENGE PROBLEM

by earth@work » Wed Oct 22, 2008 2:43 pm
Stockmoose16 wrote:Company X has n regional offices, where n represents an even integer. Each regional office must recommend two candidates, one male and one female, to serve on the corporate auditing committee. If each of the offices must be represented by exactly one member on the auditing committee and if the committee must consist of an equal number of male and female employees, how many different committees can be formed?

Image

I tried to do the problem in the following manner, but I didn't get the correct answer:

Assume N=2

That means there are 4 choices: M1, M2, F1, F2

There are 2 positions available, and one must go to a male, one must go to a female.

So you can do the following:

M1F1
M1F2
M2F1
M2F2

That means there are four total possibilities if N=2. The OA is B. If you plug in 2 for N in that equation, you do not get 4. What am I missing here?
The question says "each of the offices must be represented by exactly one member" Let, M1 & F1 belong to regional office1 and M2 &F2 belong to regional office2
So if M1, M2, F1, F2 are recommended from regional offices, but the committee can only be formed as - M1F2 or M2F1 = 2 options
we cannot take M1F1 or M2F2 as our option because here we are taking 2 members of the same regional office which is not allowed.
So taking n=2 and putting in OA n!/(0.5n!)^2 we get no. of different committees = 2 options which is correct
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Re: Combinations -- CHALLENGE PROBLEM

by Stockmoose16 » Thu Oct 23, 2008 9:35 am
earth@work wrote:
Stockmoose16 wrote:Company X has n regional offices, where n represents an even integer. Each regional office must recommend two candidates, one male and one female, to serve on the corporate auditing committee. If each of the offices must be represented by exactly one member on the auditing committee and if the committee must consist of an equal number of male and female employees, how many different committees can be formed?

Image

I tried to do the problem in the following manner, but I didn't get the correct answer:

Assume N=2

That means there are 4 choices: M1, M2, F1, F2

There are 2 positions available, and one must go to a male, one must go to a female.

So you can do the following:

M1F1
M1F2
M2F1
M2F2

That means there are four total possibilities if N=2. The OA is B. If you plug in 2 for N in that equation, you do not get 4. What am I missing here?
The question says "each of the offices must be represented by exactly one member" Let, M1 & F1 belong to regional office1 and M2 &F2 belong to regional office2
So if M1, M2, F1, F2 are recommended from regional offices, but the committee can only be formed as - M1F2 or M2F1 = 2 options
we cannot take M1F1 or M2F2 as our option because here we are taking 2 members of the same regional office which is not allowed.
So taking n=2 and putting in OA n!/(0.5n!)^2 we get no. of different committees = 2 options which is correct
Great explanation, thanks!
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