Question

in how many ways can 4 Americans and 4 English men be seated at a round table so that no two Americans may be together ​

Answer 1

The number of ways in which 4 Americans and 4 English men be seated at a round table so that no two Americans may be together ​is 144.

Step-by-step explanation:

We are given that 4 Americans and 4 English men must be seated at a round table so that no two Americans may be together.

Firstly, we know that there are a total of 8 spaces in which 4 Americans and 4 English men are to be seated.

Since no two Americans may be together, so the number of ways in which 4 Americans are to be seated = 4!

And the number of ways in which 4 English men are to be seated = (n - 1)! = (4 - 1) = 3!  {because one space would be less as no two Americans can sit together}

Hence, the required number of ways = 4! $\times$ 3!

                                                                = 24 $\times$ 6 = 144 ways.