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

  • question_answer There are 10 persons named \[A,\ B,.......J\]. We have the capacity to accommodate only 5. In how many ways can we arrange them in a line if \[A\] is must and \[G\] and \[H\] must not be included in the team of 5

    A) \[^{8}{{P}_{5}}\]

    B) \[^{7}{{P}_{5}}\]

    C) \[^{7}{{C}_{3}}(4\ !)\]

    D) \[^{7}{{C}_{3}}(5\ !)\]

    Correct Answer: D

    Solution :

    Out of 10 persons, \[A\] is in and \[G\] and \[H\] are out of the team, so we have to select 4 more from 7 remaining. This can be done in \[^{7}{{C}_{4}}\] ways. These 5 persons can be arranged in a line in \[5\ !\] ways. Hence the number of possible arrangements is \[^{7}{{C}_{4}}.\ 5\ !\ {{=}^{7}}{{C}_{3}}.\,(5\ !)\].

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