JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

  • question_answer
        The number of ways in which a committee can be formed of 5 members from 6 men and 4 women if the committee has at least one woman, is :

    A)  186                                       

    B)  246

    C)  252                                       

    D)  244

    Correct Answer: B

    Solution :

                    The number of ways can be deduce as follows: 1 woman and 4 men\[{{=}^{4}}{{C}_{1}}{{\times }^{6}}{{C}_{4}}=60\] 2 woman and 3 men\[{{=}^{4}}{{C}_{2}}{{\times }^{6}}{{C}_{3}}=120\] 3 woman and 2 men\[{{=}^{4}}{{C}_{3}}{{\times }^{6}}{{C}_{2}}=60\] 4 woman and 1 men\[{{=}^{4}}{{C}_{4}}\times 6{{C}_{1}}=6\] \[\therefore \]Required number of ways \[=60+120+60+6=246\]


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