In how many ways can lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
Given: there are 7 married couples
∴ Number of women and men = 7 each
To find: number of ways of selecting 2 men (A, B) and 2 women(C, D) such that C and D are not wives of A and B
Firstly, select 2 men out of a total of 7 men
Formula used:
Number of ways of selecting n things taken r at a time = C(n, r)
∴ Number of ways of selecting 7 things taken 2 at a time
= C(7, 2)
= 7 × 3
= 21
Now, select 2 women out of 5 men(excluding wives of A and B)
Formula used:
Number of ways of selecting n things taken r at a time = C(n, r)
∴ Number of ways of selecting 5 things taken 2 at a time
= C(5, 2)
= 5 × 2
= 10
Numbers of ways in which 4 members of the team can be chosen = 21 × 10
= 210
Now, A can choose B as team partner (⇒ C’s partner is D) or
A can choose C as team partner (⇒ B’s partner is D) or
A can choose D as team partner (⇒ C’s partner is B)
⇒ The team can be formed in these 3 possible ways
∴ Number of possible ways in which lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set = 210 × 3 = 630