Question

How many ways 5 people can be arranged in line than a circle?

Answer 1

Number of persons = 5

Arranging them in a line involves different permutations, by altering their relative positions with respect to each other.

So the number of ways = 5P5 = 5! = 120

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The number of ways of arranging them in a circular line:

     When they are standing in a circle, the arrangement in clockwise and anticlockwise do not make difference. So the total number of different ways is half of the number of ways of arranging them in a line.

     so answer for circular line:   5P5 ÷ 2   = 5! /2 = 60.

Answer 2

60 is the correct answer

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