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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?

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Question

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?

Sum
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Solution

Let two husbands A, B be selected out of seven males in 7P2  ways. excluding their wives, we have to select two ladies C,D out of remaining 5 wives is 5P2 ways.

Thus, number of ways of selecting the players for mixed double is = 7P2 × 5P2

= 21 × 10

= 210

Now, suppose A chooses C as partner (B will automatically go to D) or A chooses 0 as partner (B will automatically go to C). Thus we have, 4 other ways for teams.

Required number of ways = 210 × 4 = 840

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Factorial N (N!) Permutations and Combinations
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Chapter 16: Permutations - Exercise 16.4 [Page 37]

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R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 9 | Page 37

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