Question

In how many ways can a party of 9 persons arrange among themselves around a circular table?
a)9!
b)8!
c)9!+8!
d)none of these​

Answer 1

Answer:

This ans = 9!+8!

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Answer 2

Concept:

To solve this problem, we will need the concept of circular permutation.

Firstly, permutation is the different arrangements of a given number of things taking some or all of them at a time.

When we arrange things in the form of a circle, we call them circular permutations.

The number of circular permutations of n different objects is given by the formula: (n-1)!

Given:

We are given a party of 9 people who are to be arranged on a circular table.

To find:

We have to find the number of ways to arrange them.

Solution:

To find our desired result, let us fix the position of one person and then arrange the remaining 8 people in all possible ways.

Clearly, it can be done in 8! ways(using the formula: (n-1)! )

Hence, The required number of ways

=8!

=8x7x6x5x4x3x2x1

=40320.

Conclusion:

The number of ways to arrange 9 people in a circular table is option (b) 8!