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Problem 371

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Licence plates

Oregon licence plates consist of three letters followed by a three digit number (each digit can be from [0..9]).
While driving to work Seth plays the following game:
Whenever the numbers of two licence plates seen on his trip add to 1000 that’s a win.

E.g. MIC-012 and HAN-988 is a win and RYU-500 and SET-500 too (as long as he sees them in the same trip).

Find the expected number of plates he needs to see for a win.
Give your answer rounded to 8 decimal places behind the decimal point.

Note: We assume that each licence plate seen is equally likely to have any three digit number on it.

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汽车牌照

俄勒冈州的汽车牌照包括三个字母和一个三位数（每一位都可以取[0..9]）。
在开车上班的路上，赛斯会玩如下的游戏：
在他上班途中看到的所有汽车牌照中，如果有两个牌照上的三位数相加等于1000，则游戏获胜。

例如，MIC-012和HAN-988可以使他获胜，RYU-500和SET-500同样如此（只要他是在同一天上班途中看见的）。

求他想要获胜所需要看到的汽车牌照数的期望值。
将你的答案四舍五入到小数点后8位小数。

注意：我们假定每一个三位数在赛斯看到的每一块汽车牌照上等概率地出现。

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