Question

What is the probablitiy that a roandomly selected poermutation of the letters a, a, b, c, s, u would spell "abacus"?

Answer 1

Let Ü replace the triplet AAU in one of its permutations. There are 4!=24 ways to rearrange letters B, C, S, Ü. In each of those, there are 3 different variants of Ü, as it can be UAA, AUA and AAU. Hence, it's 3 times 24, 72 ways.

OK, seems like this is the solution you already have. Let's see what can we do about it.

You've got letters

A (x2)
B
C
U
S