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

  • question_answer
    Two friends A and B have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of A and B. The probability that all the tickets go to daughters of A is 1/20. The number of daughters each of them have is

    A)            4    

    B)            5

    C)            6    

    D)            3

    Correct Answer: D

    Solution :

               Let each of the friend have \[x\] daughters. Then the probability that all the tickets go to the daughters of \[A\] is \[\frac{{}^{x}{{C}_{3}}}{{}^{2x}{{C}_{3}}}.\] Therefore \[\frac{{}^{x}{{C}_{3}}}{{}^{2x}{{C}_{3}}}=\frac{1}{20}\Rightarrow x=3.\]


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