



 
Ian, I am not completely sure I understand the question, but maybe this will help. I think you are looking for the number of subsets of races that each contain at least two races. I'll just call these collections of races instead of subsets. Since each race is either in, or not in, a particular collection of races, there are 2^{5} = 32 possibilities. This includes the collection that contains no races. In general if you have n races, there are 2^{n} possibilities. Among the 32, there is one collection that contains no races and there are 5 that each contain a single race. This means that there are 326 = 26 collections of two or more races. When there are n races, there are 2^{n}  1  n such Victoria  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 