mathmath333
  • mathmath333
A mixed double tennis game 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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{A mixed double tennis game is to be played between two teams }\hspace{.33em}\\~\\ & \normalsize \text{(each team consists of one male and one female ).There are }\hspace{.33em}\\~\\ & \normalsize \text{four married couples . No team is to consist of a husband and }\hspace{.33em}\\~\\ & \normalsize \text{his wife. What is the maximum number of games that can be played. }\hspace{.33em}\\~\\ & a.)\ 12 \hspace{.33em}\\~\\ & b.)\ 21 \hspace{.33em}\\~\\ & c.)\ 36 \hspace{.33em}\\~\\ & d.)\ 42 \hspace{.33em}\\~\\ \end{align}}\)
mathstudent55
  • mathstudent55
Husband is A, B, C, D Wife is 1, 2, 3, 4 Married couples are: A1, B2, C3, D4 For each line below, the pair in the first column can play a match with each pair following it. For example, for the first line below, there can be matches: A2 vs B1, A2 vs B3, A2 vs B4, etc. A2 B1 B3 B4 C1 C4 D1 D3 A3 B1 B4 C1 C2 C4 D1 D2 A4 B1 B3 C1 C2 D1 D2 D3 It looks like 21 different matches.
mathmath333
  • mathmath333
answer is given is 42

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mathmath333
  • mathmath333
i think there are 12 pairs that can play matches with each other
mathmath333
  • mathmath333
is he still typing
mathstudent55
  • mathstudent55
Sorry. I though all other combinations were repeats. Let me do this again. Here are all possible matches, but some are repeats. A2 B1 B3 B4 C1 C4 D1 D3 A3 B1 B4 C1 C2 C4 D1 D2 A4 B1 B3 C1 C2 D1 D2 D3 B1 A2 A3 A4 C2 C4 D2 D3 B3 A2 A4 C1 C2 C4 D1 D2 B4 A2 A3 C1 C2 D1 D2 D3 C1 A2 A3 A4 B3 B4 D2 D3 C2 A3 A4 B1 B3 B4 D1 D3 C4 A2 A3 B1 B3 D1 D2 D3 D1 A2 A3 A4 B3 B4 C2 C4 D2 A3 A4 B1 B3 B4 C1 C4 D3 A2 A4 B1 B4 C1 C2 C4
mathstudent55
  • mathstudent55
Now we eliminate repeats. A2 B1 B3 B4 C1 C4 D1 D3 A3 B1 B4 C1 C2 C4 D1 D2 A4 B1 B3 C1 C2 D1 D2 D3 B1 C2 C4 D2 D3 B3 C1 C2 C4 D1 D2 B4 C1 C2 D1 D2 D3 C1 D2 D3 C2 D1 D3 C4 D1 D2 D3 Now the total is 42.
welshfella
  • welshfella
thats more than 42
welshfella
  • welshfella
sorry - that is 42
thomas5267
  • thomas5267
4 man and 4 women can form 16 teams. 4 teams are forbidden since there are 4 married couples. There are 12C2=66 unique ways of choosing 2 elements from a set with 12 elements. Therefore 12 teams can have 12C2=66 ways of matching and game.
thomas5267
  • thomas5267
The set of available matches are: {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {1, 8}, {1, 9}, {1,10}, {1, 11}, {1, 12}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {2, 8}, {2, 9}, {2, 10}, {2, 11}, {2, 12}, {3, 4}, {3, 5}, {3, 6}, {3, 7}, {3, 8}, {3, 9}, {3, 10}, {3, 11}, {3, 12}, {4, 5}, {4, 6}, {4, 7}, {4, 8}, {4, 9}, {4, 10}, {4, 11}, {4, 12}, {5, 6}, {5, 7}, {5, 8}, {5, 9}, {5, 10}, {5, 11}, {5, 12}, {6, 7}, {6, 8}, {6, 9}, {6, 10}, {6, 11}, {6, 12}, {7, 8}, {7, 9}, {7, 10}, {7, 11}, {7, 12}, {8, 9}, {8, 10}, {8, 11}, {8, 12}, {9, 10}, {9, 11}, {9, 12}, {10, 11}, {10, 12}, {11, 12}}
thomas5267
  • thomas5267
The size of the set is 66.
mathmath333
  • mathmath333
mathstudent's answer is correct, but i m looking for a short answer rather than listing all as mathstudent did.
anonymous
  • anonymous
@thomas5267 only problem is that A2 cannot play A3. In your scheme, these are indeed different teams but they cannot play each other. For a given team, it has only 6 other teams against which it can compete. then you have to count repeats as well.
anonymous
  • anonymous
oops, 7 other teams against which it can compete
thomas5267
  • thomas5267
Oh crap!
mathstudent55
  • mathstudent55
@thomas5267 The problem states that a man and his wife cannot form a team, so you can't form 16 teams.
thomas5267
  • thomas5267
Computer says there are 42 combinations. I calculated it using brute force.

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