Number of ways in which 8 persons can be seated on a round table so that two particular person are never together

The number of ways in which seven persons can be arranged at a round table if two particular persons may not sit together, is

Statement 1: the number of ways in which n persons can be seated at a round table, so that all shall not have the same neighbours in any two arrangements is (n-1)!//2. Statement 2: number of ways of arranging n different beads in circles is (n-1)!//2.

Find the number of ways in which six persons can be seated at a round table, so that all shall not have the same neighbours n any two arrangements.

Find the number of ways in which six persons can be seated at a round table, so that all shall not have the same neighbours n any two arrangements.

The number of ways in which six boys and six girls can be seated at a round table so that no two girls sit together and two particular girls do not sit next to a particular boy is

Prove that the number of ways in which n books can be placed on a shelf when two particular books are never together is ( n-2) xx (n-1) !

In how many ways can 6 persons be seated at a round table?

In how many ways can 5 persons be seated at a round table?

The total number of ways in which four boys and four girls can be seated around a round table, so that no girls sit together is equal to

The number of ways in which four persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements,is