Q.Of the 12 temp employees in a certain company,4 will be hired as perm employees.If 5 of the 12 temp employees are women,how many of the possible groups of 4 temp employees consist of 3 women and 1 man.
1.22
2.35
3.56
4.70
5.105
OA is D
no of groups
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Since 5 of the 12 temporary employees are women, 7 are men.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
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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Take the task of selecting the employees and break it into stages.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
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
--------------------------
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Dear Experts,
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
Experts comment please.
ash4gmat wrote:Dear Experts,
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
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The initial post was mis-worded. Look at Mitch's and Brent's cleaned up version. (There are 12 temporary employees, 4 of whom will be selected to become permanent employees.)ash4gmat wrote:Dear Experts,
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
David if 4 permanent employees have no significance then why it is mentioned in the question?
DavidG@VeritasPrep wrote:The initial post was mis-worded. Look at Mitch's and Brent's cleaned up version. (There are 12 temporary employees, 4 of whom will be selected to become permanent employees.)ash4gmat wrote:Dear Experts,
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
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It's just mentioned to give the 4-person group a label, but the label is incidental to the calculation. In essence, we have a pool of 5 women and 7 men. From this pool we want to know how many ways we can form a 4-person group of 3 women and 1 man. It just happens to be the case that those 4 people are being selected to become permanent employees. If those 4 people were being selected to form a dodgeball team or to go to the moon, etc., the math would be the same.David if 4 permanent employees have no significance then why it is mentioned in the question?
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Since 5 of the 12 temp employees are women, there are 7 male temp employees. We need to determine the number of possible groups of 4 temp employees that will consist of 3 women and 1 man. Since we have 5 female temp employees and we need to pick 3 of them, the number of ways we can do this is 5C3 since the order of their selection doesn't matter. Similarly, since we have 7 male temp employees and we need to pick only 1 of them, the number of ways we can do this is 7C1. Finally, to find number of possible groups of 4 temp employees that will consist of 3 women and 1 man, we multiply 5C3 and 7C1:ash4gmat wrote:Q.Of the 12 temp employees in a certain company,4 will be hired as perm employees.If 5 of the 12 temp employees are women,how many of the possible groups of 4 temp employees consist of 3 women and 1 man.
1.22
2.35
3.56
4.70
5.105
OA is D
5C3 x 7C1 = (5 x 4 x 3)/(3 x 2 x 1) x 7 = 10 x 7 = 70
Answer: D
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It wouldn't matter, since they're all equally likely.ash4gmat wrote:Dear Experts,
The question posted by me mentions of how many of the possible groups of 4 TEMPORARY employees consist of 3 women and 1 man.
We dont know what is the breakup of man & woman for temporary employees after 4 are made permanent.
The question as you posted it was poorly written, since the first sentence is actually redundant. (The workers haven't yet been made permanent (they *will* be hired), so we're simply asked to find the number of groups of the 12 current temps that consist of 3 women and 1 man.)