A mixed doubled tennis game is to be played between two teams (each team consists of one male and one female).

Question

A mixed doubled tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consists of a husband and his wife. What is the Maximum number of games that can be played?

Accepted Answer

Pick 2 men out of 4: C(4,2) = 6 ways. Pick 2 women out of 4: C(4,2) = 6 ways. So 6 × 6 = 36 selections of two men and two women.

For each selection of (M_a, M_b, W_p, W_q), there are 2 ways to form two teams:
  (i) (M_a, W_p) vs (M_b, W_q)
  (ii) (M_a, W_q) vs (M_b, W_p)

This gives 36 × 2 = 72 potential games.

Classify the 36 selections by how many married couples they contain:
• 0 couples (no chosen woman is the wife of a chosen man): 6 selections. Both pairings are valid → 6 × 2 = 12 valid games.
• Exactly 1 couple: 24 selections. The pairing that puts the couple on the same team is invalid; the other pairing is valid → 24 × 1 = 24 valid games.
• Exactly 2 couples (both chosen women are wives of the two chosen men): 6 selections. Pairing (i) puts both couples on the same teams (invalid); pairing (ii) gives two non-couple teams (valid) → 6 × 1 = 6 valid games.

Total valid games = 12 + 24 + 6 = 42.

Therefore, the answer is D (42).

Answer

12

Answer

21

Answer

36

Answer

42

A mixed doubled tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consists of a husband and his wife. What is the Maximum number of games that can be played?

Explanation

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