So this was a worksheet on Permutations and Combinations that you can find online, which fortunately also provides the answers. However, I am concerned because the answer provided in class is different from the online key. Here is the question:
In how many ways may 8 people form a circle for a folk dance?
For this question, can't you just factorial 8, which would be 40320 ? The student assistant in my class says that the order of the circle does not matter.
However, on the online key, the answer is ((8!)/(8))= 7! = 5040. Can someone explain how this is so?
Step-by-step explanation:
It would be 8!8! if it were a line of people, but a circle means there's no defined "start point" like there is with the line.
Since there are 88 ways to "start" the circle, there are 8!8=7!8!8=7! ways to create a unique circle of people in terms of relative ordering (i.e. where rotations do not matter).
7 votes Thanks 21
christiannyuri
for short 7 po sagot correct em if I'm wrong
Answers & Comments
Answer:
So this was a worksheet on Permutations and Combinations that you can find online, which fortunately also provides the answers. However, I am concerned because the answer provided in class is different from the online key. Here is the question:
In how many ways may 8 people form a circle for a folk dance?
For this question, can't you just factorial 8, which would be 40320 ? The student assistant in my class says that the order of the circle does not matter.
However, on the online key, the answer is ((8!)/(8))= 7! = 5040. Can someone explain how this is so?
Step-by-step explanation:
It would be 8!8! if it were a line of people, but a circle means there's no defined "start point" like there is with the line.
Since there are 88 ways to "start" the circle, there are 8!8=7!8!8=7! ways to create a unique circle of people in terms of relative ordering (i.e. where rotations do not matter).
8!
Step-by-step explanation:
I would be 8! If it were a line of people but a circle means there's no define "start point"like is there with the line.