How can fewer than 25,000 genes code for 153,000 proteins?

Answer 1

Permutations and combinations. Look it up.
But for help here is an example off the cuff:
Suppose there are only 3 gene codes and that to make a protein, I can use any 2 code, but cannot use the same one twice on a single protein.

By the above, I can easily have 6 proteins from just those 3 codes.
AB
AC
BA
BC
CA
CB

So I'm suprised that 25,000 gene codes don't have a LOT more than 153,000 proteins.