In how many ways can you seat 8 students in a row so that To

In how many ways can you seat 8 students in a row so that Tom and John never sit together?

EXPLAIN YOUR THINKING BELOW.

Solution

total ways in which 8 students can sit in a row = 8!

let us take the number of ways in which Tom and John sit next to each other i.e assuming they are always together so we have 7 students ( 6 others & 1 Tom and John) so total outcomes = 7!

so number of ways = 8! - 7! = 35280