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9th Class Mathematics Permutations and Combinations Question Bank Permutation & Combination

  • question_answer
    A committee of 5 persons is to be formed out of 6 gents and 4 ladies. In how many ways this can be done, when at most two ladies are included?

    A) 186     

    B)         168

    C) 136                     

    D)        169

    E) None of these

    Correct Answer: A

    Solution :

    Explanation Option [a] is correct. A committee of 5 persons, consisting of at most two ladies, can be formed can the following ways.
    (i) selecting 5 gents only out of 6.
    (ii) selecting 4 gents only out of 6 and one lady out of 4.
    (iii) selecting 3 gents only out of 6 and two ladies out of 4.
    In case I, the number of ways \[={{\,}^{6}}{{C}_{5}}\] In case II, the number of ways \[={{\,}^{6}}{{C}_{4}}\times {{\,}^{4}}{{C}_{2}}\] In case III, the number of ways \[={{\,}^{6}}{{C}_{5}}+{{\,}^{6}}{{C}_{4}}\times {{\,}^{4}}{{C}_{1}}+{{\,}^{6}}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}}\] \[\therefore \] Required number of ways \[=6+60+120=186\]              


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