Permutation Problem

[divi_kk]

Can someone help me with this problem:

 

At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different arrangments possible?

 

a. 5

b. 10

c. 24

d. 32

e. 120

 

The correct answer is c. 24

 

My problem is I dont understand this statement: 'Two seating arrangements are considered different only when the positions of the people are different relative to each other'

 

Thanks,

[chix475ntu]

Lets take the five postions as a,b,c,d,e - P1(person 1) can be seated in any of the five and the other persons can be seated in other 4 positions .. lets say the seating order is p1,p2,p3,p4,p5 - and p1 can be in a,b,c,d,e - so this makes 5 possible arrangements - but if you see the relative position between the persons, its the same, p5 and p2 are beside p1 etc .. so according to the stmt, this will constitute only 1 arrangement

 

HTH