circular permutation?

Question

ppl this is urgent pls answer...thanks

at a certain dinner party, ten guests are to be seated around a circular table. ho wmany different arrangements are possible?

(two arrangements are considered the same if each guest is seated between the same people)

note that 10!/2 wont work since when u think about getting the answer to 4 people around a circular table then there are 3 possible combinations.. so the formula will be [ (n-1) ! / 2 ], and to figure out ho wmany combinations are possilbe for 4 people u say..[ (4-1) ! / 2 ] = 3 possible combinations... however when i did this for 10 people i got an answer of 181440. is that rite?? cus it seems too big, and i didnt make this formula i found it on a website, however it only helped me to find the answer for 3 and 4 people.

so people pls help this is really urgent its due really soon

Answer 1

In general, the formula is (n - 1)!, but notice that an arrangement is the same when you reverse the order of the guests, so the formula will be (n - 1)!/2. In your case, 9!/2 = 181440 arrangements.

^_^

Answer 2

The way to think about circular permutations is first number the chairs. When you do this there are 10! permutations. But each permutation occurs 10 times, rotating - chair #1 has person 1, 2, 3, ...10 in it. So the total number of permutations is 9!, but reversed ones count the same, so it is 9!/2.

Answer 3

just think of it as a linear permutation, and the reverse of any arrangement counts as the same one, so really you're looking for the number of permutations, divided by two, since every arrangement has one reverse arrangement

So you just have to find P(10,10)/2. which is 10!/2

Answer 4

Brian ups is almost right. Instead of 10!/2, though, it should be 9!/2. see the link.

Answer 5

it is 10!/2=184400