Question

Consider a collection of 5 people. how many more ways can these people be arranged in a line than around a circular table?

Answer 1

96ways because in line we can arrange in 120ways where as around a circular table we can arrange in 24 ways as we want difference it is 96

Answer 2

• A collection of 5 people can be seated in 24 ways in a circular table.
• if we arranging people in a straight line seating next to each other then the combination will be 5!.
• But in case of a circular arrangement we have to fix a position for a person because every position is considered same as no one is siting in any of the table before the arrangement.
• So, in the circular arrangement if there are n person so the combinations will be (n-1)! i.e. (5-1)! = 4! =24