Need help setting up a math problem

[lennon3]

I'm looking over a practice test about to go take my test, and there is one question on the practice test that i have no clue how to set up.

"Each of 2 countries sends 6 delgates to a negotiating conference. A rectangular table is used with 6 chairs on each long side. If each country is assigned a long side of the table (operation 1), how many seating arrangements are possible?"

I'm pretty sure it has something to do with combinations, but still don't know what to do next. The answer is 1,036,800 too btw.

Thanks to anyone who understands this!

 

[ISUAgronomist]

Got it.

 

[mred]

6! * 6! * 2

Each country has 6! ways of sitting in 6 seats, so that's 6! * 6! for two countries sitting on specific sides of the table. Since there are additionally two different configurations for which country is on which side (country A side 1 country B side 2, country A side 2 country B side 1) you multiply that by 2.

 

[ISUAgronomist]

First seat has 12 choices (all others on that side will be from the same country). The other side will be your standard 6!

12*5*4*3*2*1*6*5*4*3*2*1=1036800

EDIT: What mred said would be the correct answer. I missed the "assigned" sides keyword.

 

[CycloneWanderer]

(6*5*4*3*2*1) one side
*
(6*5*4*3*2*1) other side
*
2 (delegations switch sides of the table)

 

[ist8er]

on one side : 6*5*4*3*2*1=720
on the other side : 6*5*4*3*2*1=720
both sides combined : 720*720=518,400
if the countries switched sides : 518,400*2=1,036,800

 

[ist8er]

damn...too slow

 

[lennon3]

I understand it now. Didn't really want to go into the lab for one quick question!! Thanks a lot for the help guys!

 

[CycloneWanderer]

This is fun, we should have these types of competitions regularly! CF.com math bowl.

 

[Farnsworth]

what countries are they from?

 

[Chipper]

on one side : 6*5*4*3*2*1=720
on the other side : 6*5*4*3*2*1=720
both sides combined : 720*720=518,400
if the countries switched sides : 518,400*2=1,036,800

 

[CycloneGB]

 

[CycloneWanderer]

Is this a dinner party and is anyone left-handed?

 

[Cyforce]

I came up with exactly half that number then it dawned on me.
The countries can switch sides and that gives you the answer.

 

[Farnsworth]

That would be one really long game of musical chairs.

 

[CycloneWanderer]

That would be one really long game of musical chairs.

There are still only 12 chairs :spinny:

 

[wxman1]

don't forget to carry the 2

 

[Irresponsible]

No wonder lunch always takes so long at these conferences.

 

[agrabes]

BTW, this is a Statistics problem, not a math problem

 

[lennon3]

Okay got another one for you guys, this one is probably a really easy one but confusing to me. Its the only one I missed on the practice test so I just need to figure this one out.

Given two throws of a fair die, what is the probability you get at least a 4 on each throw? At least a 5 on the first or second throw?

I got the 4 part right with 1/4. But the missed the five one. I put 2/3 and the answer is 5/9.