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

  • question_answer
    A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is      [CEE 1993]

    A)            \[\frac{1}{2}\]                          

    B)            \[\frac{5}{9}\]

    C)            \[\frac{4}{9}\]                          

    D)            \[\frac{2}{9}\]

    Correct Answer: C

    Solution :

               Required probability \[=\frac{{}^{7}{{C}_{3}}}{{}^{9}{{C}_{5}}}+\frac{{}^{7}{{C}_{5}}}{{}^{9}{{C}_{5}}}=\frac{56}{126}=\frac{4}{9}.\]


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