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

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 employees consist of 3 women and one man?

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

OA D

Source: GMAT Prep

So, there are 5 women and 7 men; out of 5 women, 3 are to be chosen and out of 7 men, 1 is to be chosen.

# of possible groups of 4 employees consist of 3 women and one man = 5C3 * 7C1 = ([5*4*3)/(1*2*3)]*7 = 70

The correct answer: D

Hope this helps!

-Jay
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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 employees consist of 3 women and one man?

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

OA D

Source: GMAT Prep

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 one can 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 one can choose 1 man from a group of 7 men is:

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

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

5C3 x 7C1 = 10 x 7 = 70

Answer: D