In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

Dear Student!

Number of Men = 7

Number of Women = 7

Number of ways to arrange 2 men out 7 men = ⁷P₂

Since, no husband and wife play in the same set, then number of ways to arrange 2 women out of 5 women (Wives of the two men can not play with same game) in ⁵P₂ ways.

Hence, by fundamental principle if multiplication,

Total number of game played = ⁷P₂ × ⁵P₂

Cheers!