At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different seating arrangements?
2006-11-12 15:50:09 · 8 answers · asked by ThinkProb 1 in Science & Mathematics ➔ Mathematics
the answers that the above people have given are wrong. the circular table does matter. let's say A, B, C, D and E are the people around the table. if they were in a line, ABCDE would not be the same arrangement as BCDEA. But in a circle, they are the same. It is unfortunate that I have forgotten what the formula is. search for it on google and you should get some answers.
hope i helped.
2006-11-12 15:58:49 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The answers giving 5! are wrong. The answer is 4! = 24, since only relative positions matter. Given where the first person sits, there are 4 options for the second person, 3 for the third, etc. Alternatively, consider the number of total ways (5!) and divide by 5 since there are 5 ways to rotate the people, which doesn't change their relative order.
If clockwise and counterclockwise arrangements aren't considered to be different, there are only 4!/2 = 12 ways.
2006-11-12 16:01:50 · answer #2 · answered by Charles G 4 · 1⤊ 0⤋
With a circular table, you can essentially eliminate the first person, as he can sit anywhere in the table. His is merely a base point to which all the other people refer. The remaining four seats can now be treated linearly, with person 1 serving as sort of a bookend on each side. Therefore the number of possibilities becomes
4! = 4 *3 * 2 * 1 = 24
2006-11-12 16:05:24 · answer #3 · answered by Robert R 2 · 0⤊ 0⤋
I think the circular table doesn't matter at all, and it is just a simple probability problem.
The answer would be the number of options for the first seat, times the number for the second, times the number for the third etc.
In other words it would be 5! (factorial)
or 5*4*3*2*1
which all comes out to 120 different seating arrangements.
2006-11-12 15:53:50 · answer #4 · answered by Anonymous · 0⤊ 1⤋
4*3*2*1
2006-11-12 17:37:42 · answer #5 · answered by gjmb1960 7 · 0⤊ 0⤋
12/24 = one million/2 are male 15/24 have dark hair (15-7)/24 = one million/3 are male and function dark hair So risk that first to realize (or any random guy or woman) could desire to have dark hair OR is a male is: one million/2 + 15/24 - one million/3 = 0.792 The one million/3 is subtracted because of the fact men that have dark hair are counted 2 cases interior the 1st 2 words.
2016-12-17 09:05:44 · answer #6 · answered by zufelt 4 · 0⤊ 0⤋
5! or 5x4x3x2x1 120 arrangements
2006-11-12 15:54:25 · answer #7 · answered by Anonymous · 0⤊ 1⤋
Just relax and everything will turn out great. Don't worry to much on having it perfect. Have it your style and that is why people like coming over...
2006-11-12 16:01:15 · answer #8 · answered by Anonymous · 0⤊ 2⤋