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sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 am; Thanked: 1 times; Followed by:1 members

Probability

by sparkle6 » Mon Oct 03, 2011 6:43 am

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

[spoiler]Answer: D. Can someone explain with combinations?[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Oct 03, 2011 6:43 am

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

by shankar.ashwin » Mon Oct 03, 2011 6:50 am

Selecting 2 women and 2 men

5/8 * 4/7 * 3/6 * 2/5 (First 2 are girls and next 2 are boys)

Now these 4 can be arranged in 4!/2!2! ways

So to consider all arrangements, multiply

5/8 * 4/7 * 3/6 * 2/5 * 4!/2!2! = 3/7

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 03, 2011 6:57 am

sparkle6 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

[spoiler]Answer: D. Can someone explain with combinations?[/spoiler]

Solution via counting methods:

P(exactly 2 women) = [# of teams with exactly 2 women] / [total # of teams possible]

# of teams with exactly 2 women
Stage 1: Select 2 women for the team. There are 5 women to choose from, so this can be accomplished in 5C2 ways.
Stage 2: Select 2 men for the team. There are 3 men to choose from, so this can be accomplished in 3C2 ways.

Total number of teams with exactly 2 women = (5C2)(3C2) = (10)(3) = 30

# of teams possible
There are 8 people altogether and we must choose 4 of them.
This can be accomplished in 8C4 ways, which equals 70 ways

P(exactly 2 women) = [30] / [70]
= 3/7 = D

Aside: To learn how to calculate combinations such as 5C2 in your head, you can watch video #17 at https://www.gmatprepnow.com/module/gmat-counting (it's free)
Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com