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

Permutations and Combinations 18/09/2021

A. 12
B. 48
C. 36
D. 42

Explanation:

Married couples = MF MF MF MF

AB CD EF GH

Possible teams = AD CB EB GB
AF CF ED GD
AH CH EH GF S

Since one male can be paired with 3 other female, Total teams = 4×3 = 12.

Team AD can play only with CB,CF,CH,EB,EH,GB,GF(7 teams )

Team AD cannot play with AF, AH, ED and GD

The same will apply with all teams, So number of total matches = 12×7 = 84.

But every match includes 2 teams, so the actual number of matches = 84/2 = 42.

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