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Math Help - Permutations and Combinations (2)

  1. #1
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    Permutations and Combinations (2)

    Q: A particular project work group of 2 girls and 3 boys meet for regular discussions at a round stone table with 6 seats. Find the number of ways the members of this group could be seated if the 2 girls insist on sitting on adjacent seats.

    The answer given to me is 48...but I don't know how to derive the answer...Thank you for helping!
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  2. #2
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    If you assume that the pattern around the table is the only thing of importance ( ie that seats are not numbered ) then seat Girl 1 anywhere.
    Girl 2 has 2 choices of adjacent seats and we have the Permutation any three from 4 remaining seats

    so 2* 4P3 = 2*24 = 48

    remember this assumes that a pattern GG_BBB where GG are in seats 1 and 2 is identical to the pattern GG_BBB where GG are in seats 3 and 4 ,but not identical to GGB_BB ( GG in seats 1 and 2)
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