Basketball Representatives

EOV wrote:Hi everybody,

Given that there are 5 basketball players per team, how many ways can you select 2 basketball
players from 3 teams if no more than one player can be selected from each team?

(A) 15
(B) 30
(C) 60
(D) 75
(E) 90

Take the task of selecting 2 players and break it into stages.

Stage 1: Select the 2 teams from which you will select 1 player each.
Since the order in which we select the 2 teams does not matter. We can use combinations.
There are 3 teams, and we must select 2 of them.
This can be accomplished in 3C2 ways (3 ways).

Stage 2: From one of the selected teams, select a player
There are 5 players on that team, so we can accomplish this stage in 5 ways.

Stage 3: From the other selected team, select a player
There are 5 players on that team, so we can accomplish this stage in 5 ways.

By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus select 2 players) in (3)(5)(5) ways ([spoiler]= 75 ways = D[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

We also have a free video on calculating combinations (like 3C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789