This should be a simple combinatorial problem. Suppose I have a number n which is a positive integer. Suppose, that there are four numbers a,b,c,d such that 0<=a<=b<=c<=d<=n. The question is how many quadruples of the form (a,b,c,d) can be formed out such arrangement? I realize that this is a homework-like question, but I am really interested in seeing which principles of combinatoris would apply here.