
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 17th, 2016, 12:17 AM  #1 
Newbie Joined: Jun 2016 From: Berlin Posts: 1 Thanks: 0  permutation of numbers and relations
How can I find the permutation for n different numbers and two relations (equal and less than)? for example for n=2 (2 different numbers), we have 3 permutation: a = b a < b b < a and for n=3 (3 different numbers), we have 13 permutation: a = b = c a = b < c a < b = c a < b < c a = c < b a < c < b b = c < a b < c = a b < c < a b < a < c c < b = a c < b < a c < a < b 
June 19th, 2016, 04:29 AM  #2 
Newbie Joined: Jun 2016 From: Hong Kong Posts: 20 Thanks: 2 
when all variables equal 1 way when all variables differ a<b<c,a<c<b,b<a<c,... n! ways when k variables equal first,choose k variables from n variables second,permute nk+1 variables say n=4,k=2,nk+1=3 a<b<c=d,a<c=d<b,c=d<a<b,... $\displaystyle C_n^k (nk+1)!$ ways $\displaystyle n!+\sum_{k=2}^{n1}C_n^k (nk+1)!+1=1+n\sum_{k=2}^n \frac{n!}{k!}$ 

Tags 
numbers, permutation, relations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Relations  rhymin  Number Theory  8  March 30th, 2013 06:18 PM 
Relations, R^2 and R^3  leafiann  Applied Math  4  March 8th, 2011 03:50 AM 
Relations, attributes, and counting to really big numbers  CRGreathouse  Applied Math  2  April 22nd, 2010 06:30 AM 
Permutation with variables & numbers  onepost  Applied Math  1  August 25th, 2009 06:29 AM 
Finding modular relations among numbers of the form 2^k + n  CRGreathouse  Number Theory  3  January 16th, 2008 07:22 AM 