# Take a gamble

Let $$S$$ be the set of all 21-digit positive integers that can be composed from the digits $$1,2,3,4,5,6,7,8,9$$ (repetition is of course allowed, but not all digits must necessarily appear). Let $$N$$ be an element of $$S$$ chosen uniformly at random, and let $$A$$ be the product of all the digits of $$N$$.

If $$P$$ is the probability that $$A$$ is divisible by $$21$$, then find $$\lfloor 1000P \rfloor$$.

×