Logic circuits are binary circuits. A single binary circuit can only be either 0 or 1. If you combine two binary circuits, you have 4 possibilities: 00,01,11,10.

3 binary circuis have 8 states and so on. You use combinatorics to know how many states a logic circuit has and to list them.

When you build a logical gate with transistors, each transistor can eiter be 0 or 1. So you use combinatorics to know all the possible states: "what is the output if the input is ..."

A binary system of n bits has 2^n states. If your bit could assume 3 states, 0, 1 and 2, then your n-bit system would have 3^n possibilities. I used combinatorics to calculate that.