2011 AIME II Problems/Problem 6

Problem:

Define an ordered quadruple (a, b, c, d) as interesting if $1≤a<b<c<d≤10$ (Error compiling LaTeX. Unknown error_msg). (Okay, if you go to edit page you can see that those wierd a's are supposed to be "less than or equal to" signs, somebody please fix this) and a+d>b+c. How many ordered quadruples are there?

---

Solution:

There is probably some really complicated formula for this, but as I didnt know it and had 3 hours to "do my best", I listed all possible combinations out. The answer is 80.