JEE Main & Advanced Mathematics Probability Question Bank Use of permutations and combinations in probability

  • question_answer
    5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternatively is  [Kerala (Engg.) 2005]

    A)            5/126                                        

    B)            1/126

    C)            4/126                                        

    D)            6/125

    E)            1/63

    Correct Answer: B

    Solution :

                       Let n = total no. of ways = 10!            m = favourable no. of ways = 2 × 5! . 5!            Since the boys and girls can sit alternately in 5 ! . 5! ways if we begin with a boy and similarly they can sit alternately in 5! . 5! ways if we begin with a girl            Hence, required probability = \[\frac{m}{n}\]                    = \[\frac{2\times 5!.5!}{10!}\]= \[\frac{2\times 5!}{10\times 9\times 8\times 7\times 6}\] = \[\frac{1}{126}\].


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