Given that there are 5 basketball players per team, how many ways can

2 teams can be selected from 3 teams in 3C2 ways = 3 ways
as the condition is that the 2 players should be from different teams
one player can be chosen from 1st team in 5 ways
similarly another player can be chosen from 2nd team in 5 ways
Total number of ways to choose the player = 5 * 5 * 3 = 75 ways
Correct Answer - D

Hi All,

If you're not comfortable with the traditional math approach to this question, you can still use 'brute force' to get to the answer rather easily.

Since we have 3 teams of 5 players each, I'm going to refer to the 3 teams of players as...

12345
ABCDE
VWXYZ

We're told that we have to pick 2 players and that we CANNOT pick them from the SAME team.

Each of the players from 12345 can be paired up with any of the players from ABCDE or VWXYZ. That's a total of 10 options per player from 12345...

(10)(5) = 50 options

Next, we can consider ABCDE. Since each of those players has already been paired up with each of the players on 12345, we don't have to consider those options. We just have to consider pairing each of the players on ABCDE with each of the players on VWXYZ. That's 5 players with 5 different pairings each:

(5)(5) = 25 additional options.

Finally, all of the players from VWXYZ have already been paired up with all of the players from 12345 and ABCDE, so there's no other options left.

50 + 25 = 75 total options

Final Answer:

GMAT assassins aren't born, they're made,
Rich

5*5 + 5*5 + 5*5 answer 75

Sent from my Lenovo A7000-a using GMAT Club Forum mobile app

A slightly different approach....

Since we're not selecting any players from one of the teams, let's "throw out" one team and then select one player from each of the remaining 2 teams.

So, take the task of selecting 2 players and break it into stages.

Stage 1: "Throw out" one team
There are 3 teams to choose from, so we can complete stage 1 in 3 ways

Stage 2: Select a player from one team
There are 5 players per team, so we can complete stage 2 in 5 ways

Stage 3: Select a player from the other team
There are 5 players per team, so we can complete stage 3 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 (= 75 ways)

Answer: D

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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Solution

Given

• Five basketball players per team and three teams are given.

To find

• The number of ways to select 2 basketball players from 3 teams if no more than one player can be selected from each team.

Approach and Working out
Since 2 basketball players are to be chosen and no more than one player can be selected from each team, thus, both players should belong to different teams.

• The number of ways of selecting two teams from 3 = \(3C_2\) = 3.

Now, we have 3 ways to select two teams out of which one player is to be selected from each team.

• Since each team has 5 players, and only one of them is to be selected, the number of ways to select a player from the first team = \(5C_1\) = 5.
• Similarly, the number of ways to select a player from the 2nd team = \(5C_1\) = 5.

Since all the above events must happen, the total number of ways = 3×5×5 = 75.

Correct Answer: Option D