Bunuel wrote:
A teacher must seat six students in 2 rows of three seats each. If the one troublesome student must sit in the front row, and the others may sit in either row, how many possible seating arrangements does the teacher have to choose from?
A. 120
B. 240
C. 300
D. 360
E. 720
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 GMAT. So, be sure to learn it.
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