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by Nijo » Sat Aug 16, 2014 12:04 am
Of the 12 temporary employees in a company, 4 will be made permanent. If 5 of the 12 temporary employees are male, how many groups of temp employees can consist of 3 women and 1 man?
1)22
2) 35
3) 56
4) 70
5) 105

OA is 70[spoiler]
Thank you very much [/spoiler]
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by GMATGuruNY » Sat Aug 16, 2014 2:38 am
The problem has been transcribed incorrectly.
It should indicate that 5 of the 12 temporary employees are WOMEN:
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 employees consist of 3 women and one man?

A. 22
B. 35
C. 56
D. 70
E. 105
Since 5 of the 12 temporary employees are women, 7 are men.
Number of ways to choose 1 man from 7 options = 7C1 = 7.
Number of ways to choose 3 women from 5 options = 5C3 = (5*4*3)/(3*2*1) = 10.
To combine the options above, we multiply:
7*10 = 70.

The correct answer is D.
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by Brent@GMATPrepNow » Sat Aug 16, 2014 6:55 am
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 employees consist of 3 women and one man?

A. 22
B. 35
C. 56
D. 70
E. 105
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, we have a free 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 ([spoiler]= 70 ways[/spoiler])

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 our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Gurpreet singh » Sun Jun 26, 2016 5:23 pm
Question stem says 5 of 12 emp are male, while the calculations have been done for female
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by DavidG@VeritasPrep » Sun Jun 26, 2016 5:27 pm
Gurpreet singh wrote:Question stem says 5 of 12 emp are male, while the calculations have been done for female
Check out Mitch's post (second from top.) He notes that the initial question had been transcribed incorrectly.
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by Gurpreet singh » Mon Jun 27, 2016 12:24 am
Sorry missed it.
Thank you.
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