JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    The number of ways of choosing a committee of two women and three men from women and six men. If Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is

    A) 60                    

    B) 84

    C) 124     

    D) none of these

    Correct Answer: C

    Solution :

    [c] (i) Miss C is taken
    [a] B included \[\Rightarrow \]A excluded \[{{\Rightarrow }^{4}}{{C}_{1}}{{\times }^{4}}{{C}_{2}}=24\]
    [b] B excluded \[{{\Rightarrow }^{4}}{{C}_{1}}{{\times }^{5}}{{C}_{3}}=40\]
    Miss C is not taken
    \[\Rightarrow \]B does not come\[{{\Rightarrow }^{4}}{{C}_{2}}{{\times }^{5}}{{C}_{3}}=60\]
    \[\Rightarrow \]Total=124
    Alternate method:
    Case I:
    Mr. B is present
    \[\Rightarrow \]A is excluded and C included
    Hence, the number of ways is \[^{4}{{C}_{2}}^{4}{{C}_{1}}=24\].
    Case II:
    Mr. 'B' is absent
    \[\Rightarrow \]No constraint
    Hence, the number of ways is \[^{5}{{C}_{3}}^{5}{{C}_{2}}\]=100.
    \[\therefore \]Total = 124.           

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