Permutation and Combination

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Aptitude miscellaneous
  1. In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position ?








  1. View Hint View Answer Discuss in Forum

    The number of arrangement in which A and B are not together
    = Total number of arrangement - Number of arrangement in which A and B are together

    Correct Option: B

    The number of arrangement in which A and B are not together
    = Total number of arrangement - Number of arrangement in which A and B are together
    = 4! - 3! x 2! = 24 - 12 = 12

  1. A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees ?








  1. View Hint View Answer Discuss in Forum

    3 girls can be be selected out of 5 girls in 5C3 ways. Since, number of boys to be invited is not given, hence out of 4 boys, he can invite them in (2)4 ways.

    Correct Option: B

    3 girls can be be selected out of 5 girls in 5C3 ways. Since, number of boys to be invited is not given, hence out of 4 boys, he can invite them in (2)4 ways.
    ∴ Required number of ways 5C3 x (2)4 = 10 x 16 = 160

  1. A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chosen ?








  1. View Hint View Answer Discuss in Forum

    Total ways = 8C3 x 8C3

    Correct Option: B

    Total ways = 8C3 x 8C3
    = (8 x 7 x 6)/(3 x 2) x (8 x 7 x 6)/(3 x 2)
    = 56 x 56 = 3136

  1. Two series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each, so that there should be no identical series side by side and that the students sitting one behind the other should have the same series ?








  1. View Hint View Answer Discuss in Forum

    As, these are two sets of booklets, so number of booklet in each set is 6 and this can be arrange in 6! ways.

    Correct Option: B

    As, these are two sets of booklets, so number of booklet in each set is 6 and this can be arrange in 6! ways.
    Also, the other 6 booklets or 2nd set can also be arranged in other 6 students in 6! ways.
    ∴ Required number of ways = 6! x 6!

  1. Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat ?








  1. View Hint View Answer Discuss in Forum

    Total number of persons = 9
    Host can sit in a particular seat in one way .
    Now, remaining positions are defined relative to the host .

    Correct Option: B

    Total number of persons = 9
    Host can sit in a particular seat in one way .
    Now, remaining positions are defined relative to the host .
    Hence, the remaining can sit in 8 places in 8P8 = 8! ways.
    ∴ The number of required arrangements = 8! x 1 = 8! = 8! ways