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

Question

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

adiagr · Accepted Answer

First select 2 group out of available 3 groups. This cane be done in 3C2 ways = 3 ways

Now from each group we have to select one person only: 5C1 * 5C1= 5 * 5 = 25

Total ways: 25 * 3 = 75 ways.

Answer D.

Divyadisha · Answer

ways to select 2 out of 3= 3

ways to select 1 player from 2 teams= 5*5

Total ways to select 1 player from 2 teams out of 3= 5*5*3= 75

D should be the answer

rhine29388 · Answer

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

EMPOWERgmatRichC · Answer

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:  D

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

HMC · Answer

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

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BrentGMATPrepNow · Answer

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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EgmatQuantExpert · Answer

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

madlol77777 · Answer

We've 15 options for Player 1, and then 10 options for Player 2 left. After, we divide by 2! since order doesn't matter. 
 (15*10)/2!=75

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

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

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