An office comprised of eight employees is planning to have a foosball

Take the task of creating a matchup and break it into stages.

Stage 1: Select 4 employees
Since the order in which we select the employees does not matter, we can use combinations.
We can select 4 employees from 8 employees in 8C5 ways (70 ways)
So, we can complete stage 1 in 70 ways

Stage 2: Divide the 4 selected employees into 2 teams
Let's say the 4 selected employees are A, B, C, D
A nice way to determine the number of ways to divide the 4 employees into 2 teams is to find a partner for one person.
For example, let's find a partner for employee A.
NOTE: once we choose a partner for employee A then, by default, the remaining two two employees will be paired together.
In how many ways can we select a partner for employee A? Well, A can be paired with B, C or D
So, we can complete stage 2 in 3 ways

ASIDE: The 3 pairings are:
AB vs CD
AC vs BD
AD vs BC

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a matchup) in (70)(3) ways (= 210 ways)

Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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