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Math Help - Combination and Permutation problem.

  1. #1
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    Combination and Permutation problem.

    The question include three parts, however I will just require help with the last part. I just find the first two parts essential for the answer.

    The number of applications for a job is 15. Calculate the number of different ways the applicants are selected for interview.(part A)
    The six selected applicants are interview in a particular day. (part B) Calculate the ways in which the order of the interviews can be arranged.
    Of six applicants interview three have background in business, two background in education and one in recreation.
    Calculate the number of ways in which the order of the six interviews can be arranged, when applicants have the SAME background are interviewed SUCCESSIVELY. ( Part 3 that i dont understand)

    I got the answer for part A to be = 15C6=5005
    and Part B to be 6!=720

    However I was unable to get the answer of part 3, I know from the back of the book that it is 72, but I have no clue why.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Consider all the applicants as being three groups, one being business, another education and last recreation.

    What you first need to see is that there is B, E and R groups (for the three groups)

    How can they be arranged? (A)

    Now, consider only the B group, there are 3 applicants. In how many ways can they be interviewed? (B)

    Consider only the E group, there are 2 applicants. In how many ways can they be interviewed? (C)

    Similarly, consider only the R group, there are 1 applicants. In how many ways can him/her be interviewed? (D)

    The anwer will be the product of A, B, C and D.

    Is that okay?
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