# combinations and a circle

#### anthonye

HI;
question: If I have 3 items how many ways can I pick them?
answer 3! = 2x2x1 = 6

problem:
question: If I have 3 items how many ways can I arrange them on a circle?
answer 2! = 2x1 = 2

I guess this has something to do with placing that first item but I don't know why,
I still have 3 items to pick at the beginning?

#### Plato

MHF Helper
HI;
question: If I have 3 items how many ways can I pick them?
answer 3! = 2x2x1 = 6

problem:
question: If I have 3 items how many ways can I arrange them on a circle?
answer 2! = 2x1 = 2

I guess this has something to do with placing that first item but I don't know why,
I still have 3 items to pick at the beginning?
The general rule is: $n$ distinct items can form $(n-1)!$ circular arrangements.
Reason: A circular arrangement of $n$ items can be rotated one place to the left $n$ times giving the same arrangement relative to the items.

• topsquark

#### mathfire

HI;
question: If I have 3 items how many ways can I pick them?
answer 3! = 2x2x1 = 6

problem:
question: If I have 3 items how many ways can I arrange them on a circle?
answer 2! = 2x1 = 2

I guess this has something to do with placing that first item but I don't know why,
I still have 3 items to pick at the beginning?