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# 4 person task force GMAT Prep problem

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4 person task force GMAT Prep problem [#permalink]  13 Jul 2009, 12:19
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Hi everybody,

I'm a new guy here on the board. It's already been very valuable in answering some of the problems from the GMAT Prep software.

Here's one I wasn't able to find searching the website.

Problem:
A 4 person task force is to be formed from 4 men and 3 women. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

a) 14
b) 18
c) 35
d) 56
3) 144

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Re: 4 person task force GMAT Prep problem [#permalink]  13 Jul 2009, 14:00
3
KUDOS

This is a combinations problem.

C^n_k = \frac{n!}{k!(n-k)!}

where n = total number of items available to select and k = number of items to be selected.

In this problem there are two distinct sets: 1 set of men and 1 set of women.

The number of ways we can select 2 (k) men from a total of 4 (n) men:

\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}

\Rightarrow C^4_2 = \frac{4!}{2!(4-2)!}

\Rightarrow C^4_2 = \frac{4!}{2!2!}

\Rightarrow C^4_2 = \frac{4 \times 3}{2 \times 1} = 6

Similarly the number of ways we can select 2 (k) women from a total of 3 (n) women:

\Rightarrow C^n_k = \frac{n!}{k!(n-k)!}

\Rightarrow C^3_2 = \frac{3!}{2!(3-2)!}

\Rightarrow C^3_2 = \frac{3!}{2!1!}

\Rightarrow C^3_2 = 3

Total number of different task forces of 2 men and 2 women possible:

= 6 \times 3

= 18
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Re: 4 person task force GMAT Prep problem [#permalink]  13 Jul 2009, 14:37
nookway's calcs are good.

Just one note about why we are using the nCr formula.

Let's label the 4 men M1, M2, M3, and M4. One possible combo is if you first choose M1, then choose M2. This team of M1 and M2 is the same as if you had chosen M2 first, then M1 second. So since M1M2 is not distinct from M2M1, order does not matter. When order does not matter, use the combination formula.
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Re: 4 person task force GMAT Prep problem [#permalink]  13 Jul 2009, 14:39
Thanks a lot!

I was looking at it as being much more complicated than it actually was.

Sorry, the OA was indeed 18.
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Re: 4 person task force GMAT Prep problem [#permalink]  03 Jul 2011, 01:20
do we need to think as they are two independent events and
to select 2 seats from 4 men is 6 and similarly to filll 2 seats from 3 women is 3....
so it is 6X3 = 18?
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Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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Re: 4 person task force GMAT Prep problem   [#permalink] 03 Jul 2011, 01:20
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