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

  • question_answer
    Ten persons, amongst whom are A, B and C to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is

    A) \[\frac{10\ !}{6}\]

    B) \[3\ !\ 7\ !\]

    C) \[^{10}{{P}_{3}}\ .\ 7\ !\]

    D) None of these

    Correct Answer: A

    Solution :

    For A, B, C to speak in order of alphabets, 3 places out of 10 may be chosen first in \[1\ .{{\ }^{3}}{{C}_{2}}=3\]ways. The remaining 7 persons can speak in \[7\ !\] ways. Hence, the number of ways in which all the 10 person can speak is \[^{10}{{C}_{3}}\ .\ 7\ !\ =\frac{10\ !}{3\ !}.=\frac{10\ !}{6}.\]

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