- #1
semidevil
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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?
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