There are seven seats in each row of a classroom. Luke and Lester are assigned to after-school detention and they must sit in the front row of the classroom, but they cannot sit next to each other because they might talk. How many ways can these two students be seated in the row?

480 Ways

Explanation:

Let z represent they must not sit together

z = (7-1) factorial ways

z = 6 factorial ways

Let x = the no. of ways the two children can be seated in 7 seats without seating next to each other

x = 2*5 factorial ways

Let y = no of ways the children can be seated on 7 seats, if the must not seat next to each other

z = x + y

y = z - x

y = 6 factorial minus 2*5 factorial

y = 6*5 factorial minus 2*5 factorial

y = 5 factorial (6-2)

y = 5 factorial times 4

y = 5*4*3*2*1*4

y = 480 ways.