Let of the 6 students be, A, B, C, D, E and T, where T represents the troublesome student.

Take the task of seating the 6 students and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select a seat for child T to sit on
We can choose any of the 3 front seats, so we can complete stage 1 in 3 ways

Stage 2: Select a seat for child A to sit on
There are 5 empty seats remaining, so we can complete stage 2 in 5 ways

Stage 3: Select a seat for child B to sit on
There are 4 empty seats remaining, so we can complete stage 3 in 4 ways

Stage 4: Select a seat for child C to sit on
There are 3 empty seats remaining, so we can complete stage 4 in 3 ways

Stage 5: Select a seat for child D to sit on
There are 2 empty seats remaining, so we can complete stage 5 in 2 ways

Stage 6: Select a seat for child E to sit on
There is 1 empty seat remaining, so we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus seat all 6 children) in (3)(5)(4)(3)(2)(1) ways (= 360 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

RELATED VIDEOS