nidhis.1408 wrote:How many ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting one of the aisles?
a. 120
b. 240
c. 360
d. 540
e. 720
Take the task of seating all 6 people and break it into stages.
Stage 1: Seat Jason
Jason must sit in one of two seats, so this stage can be accomplished in
2 ways.
Stage 2: Seat a friend
There are 5 seats remaining, so this stage can be accomplished in
5 ways.
Stage 3: Seat another friend
There are 4 seats remaining, so this stage can be accomplished in
4 ways.
Stage 4: Seat another friend
There are 3 seats remaining, so this stage can be accomplished in
3 ways.
Stage 5: Seat another friend
There are 2 seats remaining, so this stage can be accomplished in
2 ways.
Stage 6: Seat last friend
There is 1 seat remaining, so this stage can be accomplished in
1 way.
By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus seat all 6 people) in
(2)(5)(4)(3)(2)(1) ways ([spoiler]= 240 ways = B[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
