If Kristen wants to sit in an aisle seat, how many ways can they (group of 8 friends) all sit in the row?The backstory to this problem is; eight high-school friends go to the movies. They want to...

If Kristen wants to sit in an aisle seat, how many ways can they (group of 8 friends) all sit in the row?

The backstory to this problem is; eight high-school friends go to the movies. They want to sit together in a row with a student on each aisle. (Assume the row is 8 seats wide including 2 aisle seats.) I've been trying to figure the answer up for a while but i'm stumped.. A detailed explanation would be awesome, thanks! :)

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mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

There are 2 possible situations. The only condition is that Kristen sits in an aisle seat.

Situation 1: Kristen automatically gets the first seat

If Kristen sits down in seat 1, seat 2 could be occupied by any of the 7 people still standing. Seat 3 can be occupied by any one of the 6 people still standing. Seat 4 can by occupied by any one of the 5 people still standing. Seat 5 can be occupied by any one of the 4 people still standing. Seat 6 can be occupied by any one of the 3 people still standing. Seat 7 can be occupied by anyone of the 2 people still standing. Seat 8 can be occupied by the last person standing.

`1*7*6*5*4*3*2*1=5040`

Situation 2:Kristen does not get the first seat

In seat 1 any one but Kristen sits down. This means seat 1 can be occupied by any one of 7 people. This means Kristen must get seat 8. Seat 2 is occupied by any one of the 6 people still standing. Seat 3 is occupied by any one the the 5 people still standing. Seat 4 is occupied by any one of the 4 people still standing. Seat 5 is occupied by any one of the 3 people still standing. Seat 6 is occupied by any one of the 2 people still standing. Seat 7 is occupied by the last person standing. 

`7*6*5*4*3*2*1*1=5040`

In both situations, there are 5040 ways the group of 8 friends can sit with Kristen sitting in an aisle seat.

johnydan's profile pic

johnydan | Student, Grade 9 | (Level 1) Honors

Posted on

Kristen wants to sit in one of two aisle seats.

2 X 1= 2 or 2 factorial= 2

Then with 7 people left in 7 rows, it would simply be 7 factorial,

or 7 X 6 X 5 X 4 X 3 X 2 X 1.

7 factorial=5040

Then you would add them together and get

5040+2=5042

I had to think on this one too, but i believe this is the answer, but I would talk it over with someone else.

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