
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 22nd, 2013, 08:07 AM  #1 
Newbie Joined: Jul 2013 Posts: 1 Thanks: 0  Number of intersections between given sets
Assume that we have sets, with given sizes: . The (distinct) elements in each set are taken from elements (where ). A combination is defined as an assignment of distinct elements (from possible ones) to each of the sets. For example, say that we have sets of sizes and that . Then one possible combination is , another one is and so on. It is easy to note that there are possible combinations. My question is  given the sizes , how many combinations have intersection of size (denote this function of by )? My first thought was to find first how many combinations have an intersection of size at least , : My guess was that (and then ) however, the formula above for gives an over estimate. Obviously, in the first example above, it will take into account both and that are essentially the same. Any help would be greatly appreciated. 

Tags 
intersections, number, sets 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sets, intersections  kikishillong  Computer Science  2  September 30th, 2014 05:40 PM 
Number sets and creating a relationship  tbillion  Applied Math  17  September 5th, 2012 07:13 AM 
number and sets  hoyy1kolko  Algebra  4  March 15th, 2011 07:44 AM 
Number and sets  hoyy1kolko  Algebra  4  March 13th, 2011 12:00 AM 
Intersection of an infinite number of open sets (induction)  mAraujo  Real Analysis  2  July 26th, 2009 01:56 PM 