Question 1094934: How to calculate the sequence number for a license plate that has 3 Letters and 4 digits. For example what is the numerical sequence number for BJK 9999
Thank you
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) There are 10,000 plates for each 3-letter sequence;
(2) For any given first two letters, there are 26 choices for the third; so there are 26*10,000 = 260,000 plates for each sequence of the first two letters;
(3) for any given first letter, there are 26 choices for the second letter and 26 for the third; so there are 26*26*10,000 = 6,760,000 plates for each first letter.
The first letter in your example plate is B, so all of the sequences with first letter A come before this one. That's 6,760,000 of them.
The second letter in your plate is J, which is the 10th letter. So all of the plates with first two letters BA through BI will come before yours. That is another 9 times 260,000 = 2,340,000 plates.
The last letter in your plate is K, which is the 11th letter. However, since the number you chose is 9999, we can just figure out the number of plates that come before BJL0000, and that will be the "numerical sequence number" for your plate. Since L is the 12th letter, there are 11*10,000 = 110,000 plates with first two letters BJ before we get to BJL0000.
The total number of plates before BJL0000, and thus the sequence number for your plate, is
6,760,000 with first letter A;
2,340,000 with first two letters BA through BI;
110,000 with first three letters BJA through BJK0000
for a total of 9,210,000.
The numerical sequence number for plate BJK9999 is 9,210,000.
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