## anonymous 3 years ago Eight keys are placed on a key ring. How many different arrangements are possible if they are all different

1. anonymous

Pairs or ....

2. anonymous

what do you mean?

3. anonymous

just wait my Friend

4. anonymous

8 factorial

5. anonymous

|dw:1342271877443:dw| then 8 factorial as @sauravshakya

6. anonymous

my solution book says the answer is 7!/2

7. anonymous

@myko where does the 2 come from?

8. anonymous

|dw:1342272266287:dw| |dw:1342272292346:dw| is the same in this case

9. anonymous

no, you right. The right answer is 7!/2

10. anonymous

yes i thought so, because it is (n-1)!

11. anonymous

The total number of n objects, arranged in a circle which can be flipped over without making a new arrangement is: $\frac{(n-1)!}{2}$

12. anonymous

thank you@mukushla

13. anonymous

it is (n-1)! and not n!, because there is no reference point. The reference point is the first key you put, so it's has to be rested from the total number of left posibilties. It is later devided by 2, becouse the ring can flip, so symetric permutations become the same

14. anonymous

btw @myko does this rule apply to sitting in a circle arrangements