Q. 9

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

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