Question

in how many ways 5 indians and 4 americans be seated around the table if no 2 american sit together

Answer 1

Given :

Number of Indian = 5

number of American = 4

To Find :

In how many ways 5 Indian and 4 American were seated if no American sit together

Solution :

Let , The number of ways in which American are not together, = P

The number of ways in which Indian sit together = 5!

The number of ways in which American sit together = 4!

And

The number of ways in which both sit together = ( 5! × 4! )

Now,

The number of ways in which American are not together =  9! - ( 5! × 4! )  

Or,  P   =   9! - ( 5! × 4! )  

           = ( 9× 8 ×7× 6× 5× 4× 3 ×2× 1 ) -  ( 5× 4× 3 ×2× 1 × 4× 3 ×2× 1 )

           = 362880 - 2880

           = 360,000

So, The  number of ways in which American are not together = P = 360,000

Hence,  The  number of ways in which American are not together is 360,000  Answer