combinations and a circle

Jul 2010
614
5
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?


Thanks for your help.
 

Plato

MHF Helper
Aug 2006
22,490
8,653
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.
 
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Dec 2019
14
2
California
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?


Thanks for your help.
Do you mean 3!=3x2x1?
Think about whether the problem is asking for permutations or combinations.