In a badminton tournament, 9 married couples participate. A mixed doubles match requires two teams playing against each other, with each team consisting of 1 male and 1 female player. The total number of possible matches that can be organized such that exactly one married couple is among the 4 players on the court is

Step-by-step solution

We need to select 4 players (2 men and 2 women) such that exactly one married couple is among them, and then arrange them into a mixed doubles match. Step 1: Select the players. First, select the exactly 1 married couple from the 9 available couples. This can be done in ⁹C₁ = 9 ways. We now need 1 more man and 1 more woman who are not married to each other. Select 1 man from the remaining 8 couples in ⁸C₁ = 8 ways. Select 1 woman from the remaining 7 couples (excluding the spouse of the recently selected man) in ⁷C