Combinatorics

There's a branch of mathematics called combinatorics, which is essentially the science of counting. Sounds pretty simple, eh? But it ain't, not by a long shot.

Most "practical" mathematics solutions can be obtained by procedures or algorithms. Multiplying, algebra, even calculus, if you learn the procedure, you can do the math. But combinatorics isn't like that. A professor that I had called it the "thinking man's mathematics" because you can't rely on a step-by-step method to solve the problem.

Here's an example of a counting problem, very similar to one that I had in a homework problem. Let's say you were going to buy a computer. Say they come in 4 different colors, with 5 different screen sizes, and 3 different keyboard styles. How many total computer combinations are there?