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let Men & women be m1w1 , m2w2.... m4w4
total possible teams with 1 man: m1w2, m1w3,m1w4 ; 3
with 4 men ; 12 teams possible
and each team has chance to play with suppose our team is m1w2
so it can then play with
m2w1,m2w3,m2w4 ; m3w1,m3w4 ; m4w1,m4w3 ; 7 teams possible
12 *7 ; 84 matches possible
maximum matches a team can play is 84/2 ; 42
option D

Spaniard
A mixed doubles tennis game is to be played between two teams. 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.

A. 12
B. 21
C. 36
D. 42
E. 46
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I dont get why we are first choosing 2 males and then looking for people to team up with

What's wrong with my approach?
step 1: number of teams(pairs) possible
choose 1 from 4 males and choose 1 from 4 females and exclude the 4 married couples
= 4C1 * 4C1 - 4
= 12

step 2: number of games
number of games = number of teams C 2
= 12C2
= 66
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Spaniard
A mixed doubles tennis game is to be played between two teams. 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.

A. 12
B. 21
C. 36
D. 42
E. 46
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The simplest way to solve this question:

Calculate the following:
1. Number of valid teams: A valid team for a mixed doubles game implies, 1 Man and 1 Woman in the team and the 2 of them should not be married.
2. Number of games: How many games can be played among these 12 teams where there are no overlapping people while selecting the 2 teams.


Lets calculate 1:
We have 4 men and 4 women to select from.
Number of valid teams = 4*3 (each man will have 3 women teammate options - excluding his wife) = 12 teams.

Lets calculate 2:
Any team selected from the 12 teams will have 1M and 1W.

Selecting team 1:
We have 12 teams and we want to select 1 so 12C1 ways = 12 ways.

Selecting team 2:
Now the 2 people (1M & 1W) selected in team 1, cannot be a part of team 2. Any such combination would eliminate 5 teams from the 12 teams, so we are left with 7 teams, so 7C1 ways to select team 2 = 7 ways.

Total valid games = (12*7)/2 = 42 games.

Dividing by 2 because order of teams does not matter.
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