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Discussion :: Permutation and Combination

  1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

    2. A.

    564
    B.

    645
    C.

    735
    D.

    756
    E.

    None of these

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    Answer : Option D

    Explanation :

    We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

     

    Required number of ways= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
                                       

                                              =\([ \frac { 7*6*5 } { 3*2*1 }\) x \( \frac { 6*5 } { 2*1 }]\) +(7C3 x 6C1) + (7C2)

                                             

                                               = 525+\([ \frac { 7*6*5 } { 3*2*1 }\)x6]+\( [\frac { 7*6 } { 2 *1} ]\)

                                           

                                                =(525 + 210 + 21)

                                             

                                               = 756

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