AAPL wrote: ↑

Mon Aug 10, 2020 6:51 am

GMAT Prep

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

Solution:

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

AAPL wrote: ↑

Mon Aug 10, 2020 6:51 am

GMAT Prep

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

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 a 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


Cheers,
Brent