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A 4-person task force is to be formed from the 4 men and 3 w [#permalink]

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13 Jul 2009, 11:19

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A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

Re: 4 person task force GMAT Prep problem [#permalink]

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13 Jul 2009, 13:37

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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.

Re: 4 person task force GMAT Prep problem [#permalink]

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03 Jul 2011, 00:20

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

Re: 4 person task force GMAT Prep problem [#permalink]

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10 Dec 2013, 04:51

Hi,

wouldn't it suffice if we simply used 4!/2! for men and added that to 3!/1! for women?

4!/2! = 4x3 = 12 3!/1! = 6

12 + 6 = ways 4 men can fill 2 positions + ways 3 women can fill 2 positions = 18.

Why would this NOT work in general (because it works in this specific case), and why would we need to use relatively "complicated" divisions nCr formulas when the solution is much more straightforward than that?

A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. 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 E. 144

Hi,

wouldn't it suffice if we simply used 4!/2! for men and added that to 3!/1! for women?

4!/2! = 4x3 = 12 3!/1! = 6

12 + 6 = ways 4 men can fill 2 positions + ways 3 women can fill 2 positions = 18.

Why would this NOT work in general (because it works in this specific case), and why would we need to use relatively "complicated" divisions nCr formulas when the solution is much more straightforward than that?

What is the logic behind 4!/2! and 3!/1!?

The number of ways to choose 2 men out of 4 is \(C^2_4=6\); The number of ways to choose 2 women out of 3 is \(C^2_3=3\).

Principle of Multiplication says that if one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(mn\) ways.

Thus the number of ways to choose 2 men AND 2 women is 6*3=18.

Re: A 4-person task force is to be formed from the 4 men and 3 w [#permalink]

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14 Mar 2015, 19:05

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