psi20 Posted March 27, 2004 Share Posted March 27, 2004 According to what I know, if you have a circular permutation, you divide by the number of objects in the arrangement if there is no clasp. You also divide by 2 if there are reflections. Suppose you had a bracelet of 2 types of charms. One kind of charm is for luck, the other for gift. There are 2 lucks and 2 gifts arranged on this bracelet. This bracelet can not have a luck next to another luck and a gift next to another gift. It's superstitious and will give you the opposite. So you have one way to arrange it L / \ G G \ / L But according to what I know, and what my book did, you should have (2! * 2!)/(2*4) The 2!'s come from the ways to arrange the Lucks and the ways to arrange the Gifts. The 2 in the denominator comes out because it's a bracelet. The 4 in the denominator is from the total number of charms. If this is so, then there is 1/2 of a combination. The heck? Link to comment Share on other sites More sharing options...

Neurocomp2003 Posted March 27, 2004 Share Posted March 27, 2004 not a stats question, its a combinatorics question..in your case maybe finite. but i think your entire calculation is wrong. In a circular permutation you always fix one point as always... so lets say you fix 1 luck. L- _ - _ - _ then you no 2 lucks are sidebyside so *2 for the G L-2-_-_ then you need to place a luck L-2-L-_ and lastly you have tlhe last G L-2-L-1 but you have to remember you can permutate the G's by themselves so you must divide by nG! ...inthis case 2! which gives you 1*2*1*1/2! = 1; NOW LETS TRY IT YOUR WAY. 2!*2! for the permutations of the L and G.../2 cuz its a bracelet...not really sure about this one so you get 2!2!/2 = 2 you shouldn't be dividing by 4. you should be diiving by n! where n is the number of one of the 2 types. in etiher case 2! so 2!*2!/2!/2 = 1 but double check why you divide by to for it being a bracelet Link to comment Share on other sites More sharing options...

psi20 Posted April 20, 2004 Author Share Posted April 20, 2004 You divide out the 2 because it's a bracelet and can be flipped. For example, you have 3 keys on a chain. A B C If you set A as the fixed point, then A _ _ A 2 1 which means there are 2! ways, or 2 ways. But really, there is only one way. You can flip the key chain around. The A will always be adjacent to B and C. The B will always be next to C and A. Link to comment Share on other sites More sharing options...

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