3 thoughts on “Permutations II”

1. Hello,
   I am stuck on this question,
   4 boys and 4 girls sit around 2 concentric circles such that there are 4 in each circle. In how many ways can they be seated if:
   a)A particular boy is to site behind a particular girl
   b)A particular boy sits between 2 particular girls
   c)3 particular boys do not sit together

2. Try this for an idea;

   Instead of thinking of it as two circles, think of it as one circle,

   a 1
   1 d 2
   d 4 2 b becomes c 3
   3 b 4
   c a

   so part a) becomes a particular boy sits opposite a particular girl, place the boy & girl in the circle (1 way) then arrange the other six (6!)

   Total ways = 1 X 6! = 720

   and so on

3. that looked better when I typed it, so I’ll type it as a line

   a b c d
   1 2 3 4

   join d to a and 4 to 1 to create two circles, a is behind 1 etc, that is the original problem, change the problem to

   a b c d 1 2 3 4

   join 4 to a to create one circle

   hope that makes sense