A small permutation question just don't get the right answer

[chopstick]

a small permutation question...just don't get the right answer

question: 12 differently coloured beads are arranged around a necklace. how many different arrangements are possible?

the right answer on back of the book is 19958400 not 11! don't know why may be the book was wrong,
can anyone help me...

 

[Bob3141592]

Imagine that the string of the necklace breaks and all you're left with is a pile of 12 beads. Pick one at random to be the first bead, the one nearest the clasp. There are twelve choices for this, so already there will be the possibility of 12 different necklaces. Now there are 11 beads left. Pick one at random for the second bead. Now there are 12 x 11 different possible necklaces. Do this until all the beads are used, and you will have made one of the 12 X 11 X 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 possible different necklaces.

After that, find a different girlfriend to give each necklace to. I wish they gave assignments like that while I was in school!

 

[chopstick]

thanks for that,
is that normally for all possible arrangement around a circle is (n-1)!
so i think the answer should be 11!=39916800
but the right answer on back of the book is 19958400 which is half of 11!,
i am confessed...

 

[CRGreathouse]

thanks for that,
is that normally for all possible arrangement around a circle is (n-1)!
so i think the answer should be 11!=39916800
but the right answer on back of the book is 19958400 which is half of 11!,
i am confessed...

Your book considers A-B-C- the same as C-B-A-: you can flip a necklace over without changing it.

 

[regor60]

thanks for that,
is that normally for all possible arrangement around a circle is (n-1)!
so i think the answer should be 11!=39916800
but the right answer on back of the book is 19958400 which is half of 11!,
i am confessed...

Well, you can flip the necklace over and it would be indistinguishable and so there would be half of the original number, but don't know why not 12! instead of 11!

 

[chopstick]

Your book considers A-B-C- the same as C-B-A-: you can flip a necklace over without changing it.

flip?
can you give some explain please?

 

[chopstick]

i think i got it, thanks