20 students participate in a school-made olympiad: everyone has to write a question on a numbered piece of paper (from 1 to 20) and put it in a bag. The students proceed to get their to-be-solved questions by rolling a 20-sided fair dice. Let the probability that no student gets their own question be $$n$$. Find the value of $$\left\lfloor1000n\right\rfloor$$

Details and Assumptions

One question can be given to many people by the die

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