A mixed doubles tennis games is to be played between two teams (each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

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Submitted by examrobotsa on

Q: 89 (IAS/2006)
A mixed doubles tennis games is to be played between two teams (each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,0,6,3,0,3,0

keywords: 

{'mixed doubles tennis games': [0, 0, 1, 0], 'maximum number': [1, 0, 1, 2], 'games': [0, 0, 9, 4], 'married couples': [0, 0, 2, 0], 'teams': [0, 0, 4, 6]}

In this question, we`re asked to figure out the maximum number of mixed doubles tennis games that can be played between two teams. Each team is to consist of one male and one female and there are four married couples. No team should contain a husband and his wife.

Looking at the options, the correct answer given here is 42, which is option 4. This is calculated based on combination and permutation in probability theory. For the men, we have four choices and any one of them can join the team. Then, for women, we also have four choices, but we have to subtract 1 from the choices because the wife of the chosen man can`t join the team. Thus, we multiply the number of choices for men and women.

So this yields: 4 (men choices) * 3 (women choices) = 12 possible team combinations per team.

As we have two teams, the total combinations become 12*12 = 144. However, each match involves two teams, and would have been counted twice (Team AB vs Team CD is the same as Team CD vs Team AB). Thus, we divide 144 by 2 to eliminate this duplication, yielding 72.

Then we substract the 30 games where couples play against their