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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?
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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