Question

there are ten chairs in a row. in how many ways can two people be seated so that they are not seated next to each other?

Answer 1

Answer: There are 368,947,264 ways to do so.

Step-by-step explanation:

Since we have given that

Number of chairs in a row = 10

Since two people can be seated so that they are not seated next to each other.

For number 8: One sit at either end of the row  

For number 7: One sit between last and first chair.  

so, the number of ways would be

$8\times 8\times 7\times 7\times 7\times 7\times 7\times 7\times 7\times 7\\\\=8^2\times 7^8\\\\=64\times 5764801\\\\=368,947,264$

Hence, there are 368,947,264 ways to do so.