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

1. IllasMcKay

Pairs or ....

2. virtus

what do you mean?

3. IllasMcKay

just wait my Friend

4. sauravshakya

8 factorial

5. IllasMcKay

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

6. virtus

my solution book says the answer is 7!/2

7. virtus

@myko where does the 2 come from?

8. myko

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

9. myko

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

10. virtus

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

11. mukushla

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

thank you@mukushla

13. myko

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

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