## virtus Group Title Eight keys are placed on a key ring. How many different arrangements are possible if they are all different 2 years ago 2 years ago

1. IllasMcKay Group Title

Pairs or ....

2. virtus Group Title

what do you mean?

3. IllasMcKay Group Title

just wait my Friend

4. sauravshakya Group Title

8 factorial

5. IllasMcKay Group Title

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

6. virtus Group Title

my solution book says the answer is 7!/2

7. virtus Group Title

@myko where does the 2 come from?

8. myko Group Title

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

9. myko Group Title

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

10. virtus Group Title

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

11. mukushla Group Title

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. virtus Group Title

thank you@mukushla

13. myko Group Title

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. virtus Group Title

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