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The players for a Tennis Mixed Doubles match are to be chosen from

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Retired Moderator
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The players for a Tennis Mixed Doubles match are to be chosen from  [#permalink]

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New post 07 Jan 2018, 06:47
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Difficulty:

  65% (hard)

Question Stats:

38% (00:47) correct 62% (01:10) wrong based on 21 sessions

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The players for a Tennis Mixed Doubles match are to be chosen from among 5 men and 4 women. In how many ways can the teams for the match be formed?

A) 40
B) 60
C) 80
D) 120
E) 160

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Re: The players for a Tennis Mixed Doubles match are to be chosen from  [#permalink]

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New post 07 Jan 2018, 06:58
saswata4s wrote:
The players for a Tennis Mixed Doubles match are to be chosen from among 5 men and 4 women. In how many ways can the teams for the match be formed?

A) 40
B) 60
C) 80
D) 120
E) 160


As the required calculation is straightforward, we'll just do it.
This is a Precise approach.

A Mixed Double has one man and one woman per team.

Then the first team has 5C1 ways to choose the man and 4C1 ways to choose the woman.
This gives 5*4 = 20 options.
The second team then has 4C1 ways for the man and 3C1 for the woman.
This gives an additional 4*3 = 12 options.
Together we have 20*12 = 240 options.
Since there are 2 = 2! ways to pick the two teams we divide by 2 to get 120.
(Phrased differently, since we counted each team twice, we divide by two)
(D) is our answer.
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Re: The players for a Tennis Mixed Doubles match are to be chosen from  [#permalink]

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New post 07 Jan 2018, 07:51
saswata4s wrote:
The players for a Tennis Mixed Doubles match are to be chosen from among 5 men and 4 women. In how many ways can the teams for the match be formed?

A) 40
B) 60
C) 80
D) 120
E) 160


We have to choose 2 men, 2 women and then pair them up with each other (1 man, 1 woman and similarly the other pair too). So we can first choose 2 men out of 5 in 5C2 = 10 ways and choose 2 women out of 4 in 4C2 = 6 ways. Total number of ways of doing this = 10*6 = 60.

Now after this selection, we have chosen 2 men (say M1, M2) and 2 women (say W1, W2). Now for each of the above 60 cases, pairing can be done in 2 ways - either M1W1 together against M2W2 OR M1W2 together against M2W1. So total number of ways = 60*2 = 120.

Hence D answer

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: The players for a Tennis Mixed Doubles match are to be chosen from &nbs [#permalink] 07 Jan 2018, 07:51
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