Word Problem

[tltdas]

Hi.

I am working on some word problems, and just want to make sure that I am proceeding correctly.

Here is the question.

"Four married couples have reserved eight seats in a row at the theater. There are no restrictions on the seating arrangments, so how many ways can they arrange themselves?"
I though I should use 8!, so i came up with the answer of 40,320. Please let me know if I am on the right path.

Thank you,
Tara

 

[Guest]

though I should use 8!, so i came up with the answer of 40,320. Please let me know if I am on the right path.

I agree. The question isn't very clear. "Four married couples" suggests that each couple will sit together, but "There are no restrictions on the seating arrangments" suggests otherwise. Hard to tell, but I'd argue for your answer.

 

[pka]

I also agree that (8!) is the answer to the question as asked.
However, if we do require that those married to each other sit together then the answer is (2<SUP>4</SUP>)(4!).

 

[soroban]

Hello, alex and pka!

From the wording, I bet the problem has several parts.

One part is certainly "How many ways if the spouses must sit together?"

 

[pka]

Yes, I think so too!
That occurred to me only after I posted that.
I bet it is something like:
a) no restrictions
b) all men are together and all women together
c) all women together
d) no men together
e) married couples seated next to each other?

 

[Denis]

It certainly is pka's b):
the 4 guys sit together to talk football (and circulate the 40ouncer),
the 4 wives together to talk bingo