Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 11 Jul 2014, 03:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# There are 3 teams each with 5 basket players. How many combi

Author Message
TAGS:
Manager
Joined: 12 Feb 2012
Posts: 106
Followers: 1

Kudos [?]: 8 [0], given: 28

There are 3 teams each with 5 basket players. How many combi [#permalink]  01 Sep 2013, 12:16
00:00

Difficulty:

5% (low)

Question Stats:

71% (01:56) correct 28% (01:08) wrong based on 7 sessions
There are 3 teams each with 5 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?

A) 50
B) 23
C) 75
D) 28
E) 45

I know the answer is (3C2)*(5C1)*(5C1)=75
What other methods could we employ to find the same answer??

One method I am trying but its not working is: So we have 3 teams 5 each, so 15 players. I label each player by number and by team. So teams A,B,C. and the players are 1_a, 2_a,3_a,4_a,5_a, 1_b, 2_b ... 5_b, 1_c, 2_c .. 5_c.

We have a two slots. 15*14=190 permutations. But some of them are duplicates and order doesn't matter (eg. {3_a,5_c}={5_c,3_a}). So we divide by the number of slots 2!. 190/2!=95. Now we also have another constraint "No two players can be chosen from the same team". How many many ways are two 2 players from the same team are chosen? From team A we have 5 players. 5*4 ways to move them around. But again order doesnt matter so we divide by the number of slots 2!. So 10 ways. Same thing for team B and C. So we have a total of 30 ways to pick two player from the same team. from the 95 I subtract 30 to get 65. What am I doing wrong?

Are there any other ways to solve this problem other than what I laid out here?
[Reveal] Spoiler: OA
Manager
Joined: 09 Jun 2013
Posts: 54
GMAT 1: 680 Q49 V33
GMAT 2: 690 Q49 V34
GPA: 3.86
Followers: 1

Kudos [?]: 26 [0], given: 3

Re: There are 3 teams each with 5 basket players. [#permalink]  01 Sep 2013, 21:27
alphabeta1234 wrote:
There are 3 teams each with 5 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?

A) 50
B) 23
C) 75
D) 28
E) 45

I know the answer is (3C2)*(5C1)*(5C1)=75
What other methods could we employ to find the same answer??

One method I am trying but its not working is: So we have 3 teams 5 each, so 15 players. I label each player by number and by team. So teams A,B,C. and the players are 1_a, 2_a,3_a,4_a,5_a, 1_b, 2_b ... 5_b, 1_c, 2_c .. 5_c.

We have a two slots. 15*14=190 permutations. But some of them are duplicates and order doesn't matter (eg. {3_a,5_c}={5_c,3_a}). So we divide by the number of slots 2!. 190/2!=95. Now we also have another constraint "No two players can be chosen from the same team". How many many ways are two 2 players from the same team are chosen? From team A we have 5 players. 5*4 ways to move them around. But again order doesnt matter so we divide by the number of slots 2!. So 10 ways. Same thing for team B and C. So we have a total of 30 ways to pick two player from the same team. from the 95 I subtract 30 to get 65. What am I doing wrong?

Are there any other ways to solve this problem other than what I laid out here?

There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 25 possibilities (5*5) since each team has 5 players. So there are a total of 75 possibilities (25*3). I hope this method is easier for you to understand.
_________________

Don't be afraid to fail, but be afraid not to try

Re: There are 3 teams each with 5 basket players.   [#permalink] 01 Sep 2013, 21:27
Similar topics Replies Last post
Similar
Topics:
How many ways can you distribute 5 marbles in 3 baskets 0 16 Jun 2013, 06:01
2 A football team has 99 players. Each player has a uniform nu 2 08 Feb 2013, 19:12
15 How many different 5-person teams can be formed from a group 11 22 Jun 2010, 18:14
There are 5 players on the basketball team. What is the 1 11 Nov 2006, 00:33
7 basketball teams with five players each are at a 1 10 Oct 2006, 09:58
Display posts from previous: Sort by