Please help if you can...

In how many ways can 7 people be seated in a row of 9 chairs if Jane and Joe must sit next to each other?

Dominator416 Dec 16, 2018

#1**+2 **

Please help if you can...

In how many ways can 7 people be seated in a row of 9 chairs if Jane and Joe must sit next to each other?

Just consider that there are 8 chairs and 6 people.

2* 8P6

2 * 20160 = 40,320 ways.

I think that is right.

Melody Dec 16, 2018

#2**+3 **

Note that Jane and Joe can occupy any of 8 positions

12

23

34

45

56

67

78

89

And they can be seated in 2 ways for each of these

And note that, for each of these positions, we will have 7 other seats available for the other 5 people to sit in

Call these other empty seats A B C D E F G

So....we can assign any 5 of these for the other people to sit in

And we can permute these in P(7, 5) ways = 2520 ways

So....the total ways =

8 * 2 * 2520 = 40,320 ways

CPhill Dec 16, 2018