A small company employs 3 men and 5 women. If a team ....

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

A small company employs 3 men and 5 women. If a team ....

by factor26 » Sun Jan 15, 2012 4:06 pm

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a- 1/14
b- 1/7
c- 2/7
d- 3/7
e- 1/2

Answer is D can someone please show how to solve in detail? Thanks

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Source: Beat The GMAT — Data Sufficiency | Sun Jan 15, 2012 4:06 pm

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Sun Jan 15, 2012 4:12 pm

Posted a solution here
https://www.beatthegmat.com/probability-t92247.html

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VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 am; Location: Los Angeles, CA; Thanked: 474 times; Followed by:365 members

by VivianKerr » Sun Jan 15, 2012 5:58 pm

For the first choice, we want any 3/8. For the second choice, we want any 2/7. For the third choice, we can any 5/6. For the last choice, we want any 4/5. The probability of one option is the product: 120/1680 = 1/14. So there is a 1/14 chance of getting "exactly" 2 men and 2 women.

But now we have to consider that we are choosing 2 men and 2 women from 4 slots total, so we have to do a combination to find the possible arrangements of these selections.

4! / 2! (4 - 2)! = 4 x 3 x 2 / 2 x 2 = 24/4 = 6 ways.

So we multiply 1/14 by 6 since any 6 arrangements will do: 1/14*6 = 6/14 = 3/7.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun Jan 15, 2012 8:20 pm

I posted a solution here:

https://www.beatthegmat.com/select-exact ... 88786.html

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sun Jan 15, 2012 10:16 pm

factor26 wrote:A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a- 1/14
b- 1/7
c- 2/7
d- 3/7
e- 1/2

Answer is D can someone please show how to solve in detail? Thanks

Probability = Number of ways an event can occur/ Total number of possible outcomes
Total number of employees = 8
4 employees are to be selected randomly, so total number of possible outcomes = 8C4 = 8!/(8 - 4)! * 4! = 70
Now exactly 2 women are to be selected implies that there should be exactly 2 men, so number of ways of selecting exactly 2 women = 5C2 * 3C2 = [5!/(3! * 2!] * [3!/2!] = 10 * 3 = 30

Therefore, required probability = 30/70 = [spoiler]3/7[/spoiler]

The correct answer is D.

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