How many people can sit in a row? circle?

[babowc]

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Getting some conflicting answers here.. unless there's different permutation formula for sitting in a row or a circle.

Math destroyer Q: How many different ways (orders) can 5 people stand in line?
A: 5! = 120

Top score Q: How many arrangements can 6 people can be seated round a circular table?
A: 5! = 120

Is there a difference between a row, and a circle?
I thought answer to the latter, was 720... (6!)

 

[J777]

Yeah, there is a difference. When sitting in a circle, some of the arrangements you'd get when doing a simple factorial calculation are double counted. Take the linear example first. With 3 people, A, B and C, you can arrange them as ABC, ACB, BAC, BCA, CAB, and CBA (3! = 6). However, if sitting at a table, many of these arrangements are actually the same thing (such as ABC and CAB.. draw it out if is unclear). Thus, we must take the double-counting into consideration.

Just remember that if in a circle of n people, there are (n-1)! ways to arrange them. So in your example (n-1)! = (6-1)! = 5! = 120.

You can also think of it as n!/n.. Same thing: 6!/6 = 5! = 120

 

[tayloreve]

hahah i had the same problem...i was like wtf? but good to know..


LINE.....n!
CIRCLE..(n-1)!

I hope i have one of these on the QR section 😀

 

[babowc]

hahah i had the same problem...i was like wtf? but good to know..


LINE.....n!
CIRCLE..(n-1)!

I hope i have one of these on the QR section 😀

DITTO!!!

 

[SodiumChanel]

ohh...good question! babwc, whens your exam? I can see that you're posting quite a lot here haha which is good!! mine is coming up too. yikes..

 

[babowc]

ohh...good question! babwc, whens your exam? I can see that you're posting quite a lot here haha which is good!! mine is coming up too. yikes..

It's in 22 hours.

 

[tayloreve]

It's in 22 hours.

mine is tomorrow too!!!!!!!! i can't wait to hear from you! i'm super nervous too...but also ready to get it over with! lol. we're going to do great 🙂

 

[babowc]

mine is tomorrow too!!!!!!!! i can't wait to hear from you! i'm super nervous too...but also ready to get it over with! lol. we're going to do great 🙂

Let's kill it👍
Goodluck!
I think I've wrapped up doing math/sns.. now to go on to some PAT action for a little, and review!

 

[SodiumChanel]

Let's kill it👍
Goodluck!
I think I've wrapped up doing math/sns.. now to go on to some PAT action for a little, and review!

good luck to you two! Mine is the day after yours hahaha. Let's hear about it afterwards!!