## Licence plates

### Problem 371

Published on Sunday, 12th February 2012, 10:00 am; Solved by 831; Difficulty rating: 30%
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.