- #1

semidevil

- 157

- 2

update:

*edit: solved! I counted everything twice.

How many ways are there to seat 10 people, consisting of 5 couples, in a row

of seats (10 seats wide) if all couples are to get adjacent seats?

I'm trying to look calculate it at a couple level.

10 seats available, 5 couples

_ _ _ _ _ _ _ _ _ _

first couple has 9 choices to choose from They can't choose seat # 10 or else they will not sit next to each other. they can also swap seats, so that will be 9 x 2 = 18 choices.

second couple will have 7 seats to choose from. They can trade seats, so that will be 7 x 2 = 14

third couple has 5 seats, trade seats an yield 10.

fourth couple has 3 seats, = 6

5th couple has 2 seats left, they can trade once, so that is 2 possibilities

I did 18 x 14 x 10 x 6 x 2 = 30,240. answer key says 3840 though?

*edit: solved! I counted everything twice.

## Homework Statement

How many ways are there to seat 10 people, consisting of 5 couples, in a row

of seats (10 seats wide) if all couples are to get adjacent seats?

## The Attempt at a Solution

I'm trying to look calculate it at a couple level.

10 seats available, 5 couples

_ _ _ _ _ _ _ _ _ _

first couple has 9 choices to choose from They can't choose seat # 10 or else they will not sit next to each other. they can also swap seats, so that will be 9 x 2 = 18 choices.

second couple will have 7 seats to choose from. They can trade seats, so that will be 7 x 2 = 14

third couple has 5 seats, trade seats an yield 10.

fourth couple has 3 seats, = 6

5th couple has 2 seats left, they can trade once, so that is 2 possibilities

I did 18 x 14 x 10 x 6 x 2 = 30,240. answer key says 3840 though?

Last edited: