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

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.

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A (x2)

B

C

U

S