Question

In how many ways can 10 persons can be seated along round table with
5 seats​

Answer 1

Step-by-step explanation:

The number of ways 10 people can be seated abreast = 10! = 3,628,800.

This is also the number of ways that 10 people can be seated at a round table if we choose a particular point to be the beginning and end of the row. But there are 10 possible such points. So there are 10 ways of seating 10 people abreast for every way of seating them at a round table. It follows that the number of ways of seating 10 people at a round table = 10!/10 = 9! = 362,880.

For example, suppose the 10 people are represented by the letters A, B, C, D, E, F, G, H, I and J.

Then if A, B, C, D, E, F, G, H, I and J sit in this order at a round table, this is the same as:

B, C, D, E, F, G, H, I, J and A;

C, D, E, F, G, H, I, J, A and B ;

…

J, A, B, C, D, E, F, G, H and I.