Question 1207576: At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if one seating can be obtained from rotating the other.)
Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website! .
At a meeting, four scientists, two mathematicians, and a journalist are to be seated
around a circular table. How many different arrangements are possible if the mathematicians
must sit next to each other? (Two seatings are considered equivalent if one
seating can be obtained from rotating the other.)
~~~~~~~~~~~~~~~~~~~~~~
In all, there are 4+2+1 = 7 persons in this experiment.
As usual for such problems, we will consider the glued pair (Matn,Math) as one object,
so we have 7-1 = 6 objects in this problem.
For 6 objects, there are (6-1)! = 5! = 120 different circular permutations.
We should double this value for the final answer to account for two different possible
positions of these two mathematicians, (A,B) and/or (B,A), which are not equivalent at rotations.
ANWER. There are 2*5! = 2*120 = 240 different arrangements in this problem.
Solved.
|
|
|
