Take the task of creating the team and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select a boy to be goalkeeper
We can choose any of the 3 boys who can only be goalkeeper, so we can complete stage 1 in 3 ways

Stage 2: Select 3 defenders
There are 9 boys who can play any non-goaltender position
Since the order in which we select the 3 defenders does not matter, we can use combinations.
We can select 3 boys from 9 boys in 9C3 ways (84 ways)
So, we can complete this stage 84 ways

Stage 3: Select 3 midfielders
Since we already selected 3 of the 9 boys in stage 2, there are now 6 boys remaining
Since the order in which we select the 3 midfielders does not matter, we can use combinations.
We can select 3 boys from 6 boys in 6C3 ways (20 ways)
So, we can complete this stage 20 ways

Stage 4: Select 1 forward
There are now 3 boys remaining
So, we can select 1 forward in 3 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an 8-person team) in (3)(84)(20)(3) ways (= 15,120 ways)

Answer: E

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

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