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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In a sports club, 6 players are divided into 3 teams of 2 pl tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 0 member replies ### GMAT/MBA Expert ## In a sports club, 6 players are divided into 3 teams of 2 pl ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] In a sports club, 6 players are divided into 3 teams of 2 players. How many such arrangements are possible? A. 10 B. 15 C. 25 D. 30 E. 40 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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The usage of the term arrangements is misleading. The prompt seems intended to ask the following:

Quote:
How many ways can 6 players be divided into pairs?

A. 10
B. 15
C. 25
D. 30
E. 40
The first player selected can be paired with any of the 5 other players.
Thus, the number of options for the first player selected = 5.
At this point, 4 players remain.
The next player selected can be paired with any of the 3 other players.
Thus, the number of options for the next player selected = 3.
The 2 remaining players must serve as the final pair.
To combine the options in blue, we multiply:
5*3 = 15.

The correct answer is B.

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### GMAT/MBA Expert

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Mitch has a good point. We will follow his suggestion.

Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

In a sports club, 6 players are divided into pairs. How many such arrangements are possible?

A. 10
B. 15
C. 25
D. 30
E. 40
$$?\,\,\,:\,\,\,\# \,\,{\rm{pairs}}\,\,{\rm{among}}\,\,6\,\,{\rm{people}}$$
$${\rm{If}}\,\,{\rm{teams}}\,\,\left( {{\rm{pairs}}} \right)\,\,A,B,C\,\,{\rm{are}}\,\,{\rm{distinguishable:}}$$
$$\underbrace {C\left( {6,2} \right)}_{{\rm{team}}\,\,A}\,\,\,\, \cdot \,\,\,\underbrace {C\left( {4,2} \right)}_{{\rm{team}}\,\,B}\,\,\,\, = \,\,\,\,{{6 \cdot 5} \over 2} \cdot {{4 \cdot 3} \over 2} = 15 \cdot 6 = 90\,\,\,\,\,\left[ {{\rm{team}}\,\,{\rm{C}}\,\,{\rm{ = }}\,\,{\rm{remainder}}\,\,{\rm{players}}} \right]$$
$${\rm{Filtering}}\,\,\left( {{\rm{same}}\,\,{\rm{pairs}}\,\,{\rm{at}}\,\,{\rm{different}}\,\,{\rm{named}}\,\,{\rm{teams}}} \right)\,\,\,{\rm{:}}\,\,\,\,\,? = {{90} \over {3!}} = 15$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Since we need to choose 2 players out of 6 players for the first team, choose 2 players out of 4 players for the second team and choose 2 players out of 2 players for the last team, the number of possible choices, in this order is 6C2*4C2*2C2.
Since the order in which the three teams is chosen does not matter, we need to divide this by the number of arrangements of these 3 teams, which is 3!.
Thus, the number of possible arrangements is 6C2*4C2*2C2/3! = 15*6/6 = 15

Therefore, the answer is B.
Answer: B

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Max@Math Revolution wrote: [Math Revolution GMAT math practice question] In a sports club, 6 players are divided into 3 teams of 2 players. How many such arrangements are possible? A. 10 B. 15 C. 25 D. 30 E. 40 The number of ways to select the first team is 6C2 = (6 x 5)/2! = 15 The number of ways to select the second team is 4C2 = (4 x 3)/2 = 6 The number ways to select the last team is 2C2 = 1 Since order does not matter for the team selection, the number of ways to select the teams is: (15 x 6 x 1)/3! = 15 ways Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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