JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    The numbers of permutations of \[n\] things taken \[r\] at a time, when \[p\]things are always included, is

    A) \[^{n}{{C}_{r}}\ p\ !\]

    B) \[^{n-p}{{C}_{r}}\ r\ !\]

    C) \[^{n-p}{{C}_{r-p}}\ r\ !\]

    D) None of these

    Correct Answer: C

    Solution :

      Since number of selections are \[^{n-p}{{C}_{r-p}}.\] Therefore the arrangement of r things can be done in r ! ways. Hence the total permutations are \[^{n-p}{{C}_{r-p}}\,r\,!\]


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