M22-04

Question

6 male and 8 female employees work in the IT department. If an expert group has to be formed including 2 men and 1 woman, how many variants are possible?

A. 60
B. 80
C. 120
D. 150
E. 180

Bunuel · Answer

Official Solution:

6 male and 8 female employees work in the IT department. If an expert group has to be formed including 2 men and 1 woman, how many variants are possible?

A. 60
B. 80
C. 120
D. 150
E. 180

C_{6}^2 * C_{8}^1 = \frac{6!}{(4!2!)}*8 = 15 * 8 = 120 .

Answer: C

bhavik29 · Answer

Hello,

I know this is a dumb question, but where do you get the 6 from? I need to brush my fundamentals with permutations and combinations.

Bunuel · Answer

Hello,

No question is dumb when you're trying to understand a concept! In this problem, the 6 comes from the total number of male employees in the IT department. You're trying to form an expert group that includes 2 men out of the 6 male employees available, so the combination is denoted by  C_{6}^2 , which represents the number of ways to choose 2 men out of 6.

In general, for combinations,  C_{n}^k=\frac{n!}{k!(n-k)!}  represents the number of ways to choose  k  items out of  n  without regard to the order. In this case,  n = 6  (the total number of male employees) and  k = 2  (the number of male employees you want to include in the group).

Hope it's clear.

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M22-04

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