The problem of calculating how many permutations three A's and two B's can form (such as AAABB, AABBA) is the research leader of combinatorial mathematics.
The answer is 16. Solve by interpolation. | A |A | A |, put the first b in four spaces. There are four ways to put the second B and five ways to put it, but it is the same before or after the second B, so it is actually four. Therefore, the total number of permutation is 4*4= 16.