$input is just a scalar. It has the range 0..$max. I don't see where a factorial of the count comes in.

The idea is:

shuffle(42, 10, 0) == 6
shuffle(42, 10, 1) == 1
shuffle(42, 10, 2) == 5
shuffle(42, 10, 3) == 8
shuffle(42, 10, 4) == 3
shuffle(42, 10, 5) == 4
shuffle(42, 10, 6) == 9
shuffle(42, 10, 7) == 2
shuffle(42, 10, 8) == 7
shuffle(42, 10, 9) == 0
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?

-Andrew.