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

  • question_answer
    A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are  put into a hat and 11 drawn at random, then the chance of obtaining an eleven containing at least 3 bowlers is

    A)   \[\frac{7}{13}\]                                 

    B)   \[\frac{11}{15}\]

    C)            \[\frac{12}{13}\]                     

    D)            None of these

    Correct Answer: C

    Solution :

                       Required probability                                                                  \[=\frac{{}^{5}{{C}_{3}}\times {}^{10}{{C}_{8}}}{{}^{15}{{C}_{11}}}+\frac{{}^{5}{{C}_{4}}\times {}^{10}{{C}_{7}}}{{}^{15}{{C}_{11}}}+\frac{{}^{5}{{C}_{5}}\times {}^{10}{{C}_{6}}}{{}^{15}{{C}_{11}}}=\frac{12}{13}\].


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