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Of the 12 temporary employees in a certain company, 4 will

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Of the 12 temporary employees in a certain company, 4 will

by BTGmoderatorDC » Tue Jun 04, 2019 5:54 pm

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Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

A. 22
B. 35
C. 56
D. 70
E. 105

OA D

Source: Official Guide
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by Brent@GMATPrepNow » Wed Jun 05, 2019 4:55 am
BTGmoderatorDC wrote:Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

A. 22
B. 35
C. 56
D. 70
E. 105

OA D

Source: Official Guide
Take the task of selecting the employees and break it into stages.

Stage 1: Select the 3 women
The order in which we select the women does not matter, so we can use combinations.
We can select 3 women from 5 women in 5C3 ways (= 10 ways)

Aside: If anyone is interested, here's video on calculating combinations (like 5C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 2: Select the 1 man
There are 7 men, so we can complete this stage in 7 ways.

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select the permanent employees) in (10)(7) ways (= 70 ways)

Answer: D
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat-counting?id=775

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Wed Jun 05, 2019 2:36 pm
Total number of Women \(= 5 \)
Total Number of Men \(= 4\)

No of employers to be hired \(- 04\)
No. of Women employees to be hired \(- 03\) (Given in the question)
No. of Men to be hired \(- 1\) (given in the question)

Therefore number of Combinations \(= C(5,3) \cdot C (7,1) = 10 \cdot 7 = 70\)
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by Scott@TargetTestPrep » Thu Jun 06, 2019 4:59 pm
BTGmoderatorDC wrote:Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

A. 22
B. 35
C. 56
D. 70
E. 105

OA D

Source: Official Guide
We are asked to find the number of ways of choosing 3 women from a group of 5 women and 1 man from a group of 7 men.

Let's first find the number of ways to choose 3 women from 5. Since the order of how the 3 women are chosen doesn't matter, we use combinations:

5C3 = 5!/(3! x 2!) = (5 x 4 x 3)/3! = 60/6 = 10

Similarly, the number of ways to choose 1 man from a group of 7 men is:

7C1 = 7!/(1! x 6!) = 7

Finally, the number of ways to choose 3 women from 5 women and 1 man from 7 men is:

5C3 x 7C1 = 10 x 7 = 70

Answer: D

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