As a child I had a bike with the alphanumeric serial AD93847. A few weeks ago I registered with a web service and was issued the registration Alphanumeric AD93847 - Identical to the bike reg. What is the probability for this happening?
Assuming both serial numbers are restricted to two letters followed by five numerical digits, then the number of ways of constructing such a serial number is
26 X 26 x 10 X 10 X 10 X 10 X 10 = 67, 600, 000
so the odds against it happenig are 1 in 67,600,000