JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:

    A) 40

    B) 41

    C) 16

    D) 32

    Correct Answer: B

    Solution :

    [b] Require number of ways \[{{=}^{2}}{{C}_{1}}{{\times }^{2}}{{C}_{1}}{{\times }^{4}}{{C}_{2}}{{+}^{2}}{{C}_{1}}{{\times }^{2}}{{C}_{2}}{{\times }^{4}}{{C}_{1}}\] \[{{+}^{2}}{{C}_{2}}{{\times }^{2}}{{C}_{1}}{{\times }^{4}}{{C}_{1}}{{+}^{2}}{{C}_{2}}{{\times }^{2}}{{C}_{2}}{{\times }^{4}}{{C}_{0}}\] \[=2\times 2\times \frac{4\times 3}{2}+2\times 1\times 4+1\times 2\times 4+1\times 1\times 1\] \[=24+8+8+1=41\]


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