JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer In how many ways can a committee be formed of 5 members from 6 men and 4 women if the committee has at least one woman [RPET 1987; IIT 1968; Pb. CET 2003]

    A) 186

    B) 246

    C) 252

    D) None of these

    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 women and 3 men \[{{=}^{4}}{{C}_{2}}{{\times }^{6}}{{C}_{3}}=120\] 3 women and 2 men \[{{=}^{4}}{{C}_{3}}{{\times }^{6}}{{C}_{2}}=60\] 4 women and 1 man \[{{=}^{4}}{{C}_{4}}{{\times }^{6}}{{C}_{1}}=6\] Required number of ways\[{{=}^{7}}{{C}_{4}}=35\].

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