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

  • question_answer
    A man has three friends. The number of ways he can invite one friend every day for dinner on six successive nights so that no friend is invited more than three times is

    A) 640      

    B) 320

    C) 420                 

    D) 510

    Correct Answer: D

    Solution :

    [d] Let x, y, z be the friends and a, b, c denote the case when x is now, we have the following possibilities: (a, b, c) = (1, 2, 3) or (3 3 0) or (2 2 2) [grouping of 6 days of week] Hence, the total number of ways is \[\frac{6!}{1!2!3!}3!+\frac{6!}{3!3!2!}3!+\frac{6!}{(2!2!2!)}3!\]

You need to login to perform this action.
You will be redirected in 3 sec spinner