Question

describe why circular permutations are different from linear permutaions

Answer 1

A linear permutationis the usual kind; 1-2-3, 1-3-2, 2-3-1, 2-1-3, 3-1-2, 3-2-1.

Can you describe what a circular permutation is?

Answer 2

it's the number of ways to arrange distinct objects along a fixed circle is

Answer 3

So let's take a linear permutation of 4 items. How many (linear) permutations are there (as an expression, don't multiply it out yet)

Answer 4

Let's look at the first permutation: 1-2-3-4:
There are four _identical_ circular permutations for this one linear permutation, right?

Answer 5

yes, so what is the difference between the two?

Answer 6

Well, not to be a smart alec,but that's the part you are supposed to be figuring out, isn't it?

Take the formula for linear permutation.
Note that if you have X linear permutations for n positions, you have _fewer_ circular permutations, because there are n identical linear permutations of each circular permutation. There are X/n circular permutations.

Figure what X is, plug it in. HINT: I say you solve 'the same' problem that this reduces to, about 20 minutes ago with @mathstudent55 You can figure this out.

Answer 7

okay thank you

Answer 8

Sorry, I misread the question, to describe why. Did you figure out why? If you join the ends of a linear into a circle, what happens? Can you explain why 1/n permutations are now identical?