Help with review for math test <span title="(permutations/combinations)?">(permutations/combination...</span>

Question

I am taking business mathematics, and doing quite well. I have been able to answer all my own questions thus far, but came across a question that has stumped me. I have been working for hours trying to find the answer with no luck. Maybe someone can help.

Please note: I am not looking for anyone to do my homework, I am looking for the methodology that is needed to complete this problem. I had a similar problem on my online quiz through MyMathLab, but it did not explain how to do it, it only gave me the answer after I finished. I am looking for how the answer was achieved so I can use this knowledge in case there is a similar question on the test.

Here is the problem:

Each of 2 countries sends 5 delegates to a negotiating conference. A rectangular table is used with 5 chairs on each long side. If each country is assigned a long side of the table (operation 1), how many seating arrangements are possible?

Answer 1

each country can be assigned to 1 of 2 sides

X = 2*.......

the first delegate from canada can sit in 1 of 5 seats

the second can sit in 1 of 4 seats

the third in 1 of 3 seats........

X= 2(side of table ) * (5*4*3*2*1)(canadian delegates )

same for the chinese delegates

X=2(sides of table ) * (5*4*3*2*1)(canada) * (5*4*3*2*1)(china)

so X = 2 * (5!) * (5!)

(5! = 5*4*3*2*1)

Answer 2

alright so each country has one side of the table and 5 people which cannot go on the other side

Each side of the table can have 25 different arrangements while the other side can have 25 as well

5*5

so you then multiply 25*25 because there is 25 different ways each could be set up while the other stays the same

Answer-625 different arrangements

Hope this helped :)

Answer 3

what was the answer?

Answer 4

The first country can be arranged in 5! ways and so can the second country.  So multiply these two together and get (5!)^2

Answer 5

2 * 5! * 5!

= 2*120*120

=28800

2 because either of the country can be assigned 1 side.

5! for seating arrangements for each country.