JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    Number of ways in which a lawn-tennis mixed double be made from seven married couples if no husband and wife play in the same set is

    A) 240                  

    B) 420

    C) 720                 

    D) none of these

    Correct Answer: B

    Solution :

    [b] We first select 2 man out on 7 in \[^{7}{{C}_{2}}\]ways. Now we exclude the wives of these two selected men and so select 2 ladies form remaining 5 ladies in \[^{5}{{C}_{2}}\]ways. Let A, B be two men and X, Y be the ladies playing in one set. Then we can have  (i) A and X plying against B and Y.  (ii) A and Y playing against B and X. Then the total number of ways is \[^{7}{{C}_{2}}{{\times }^{5}}{{C}_{2}}\times 2=21\times 10\times 2=420\].

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