Combinatorics - How many combinations out of two groups?

Bens4vcobra wrote:A 4 person task force is to be formed from 4 men and 3 women who work in Company G's HR dept. If there are to be 2 men and 2 women, how many different task forcers can be formed?
A)14
B)18
C)35
D)56
E)144

We can take the task of "building" a task force and break it into stages.

Stage 1: select the 2 women for the team
Stage 2: select the 2 men for the team

Stage 1: since the order of the selected women does not matter, this is a combination question.
There are 3 women, and we want to choose 2 of them.
This can be accomplished in 3C2 ways, which equals 3

Stage 2: since the order of the selected men does not matter, this is a combination question.
There are 4 men, and we want to choose 2 of them.
This can be accomplished in 4C2 ways, which equals 6

At this point, we can apply the Fundamental Counting Principle and find the product of the two stages to get (3)(6) = 18

So the answer is B

Cheers,
Brent

PS: To learn a shortcut for calculating combinations in your head, see https://youtu.be/-bbu2h-07iA

Bens4vcobra wrote:A 4 person task force is to be formed from 4 men and 3 women who work in Company G's HR dept. If there are to be 2 men and 2 women, how many different task forcers can be formed?
A)14
B)18 (correct answer)
C)35
D)56
E)144

Number of different task forces = (Number of ways to select 2 men out of 4)*(Number of ways to select 2 women out of 3) = (4C2)*(3C2) = 6*3 = 18

The correct answer is B.