# Number Plate Problem

I'm having trouble with a question that seems to perplex: A number plate contains three letters followed by three numbers. A number plate is selected at random. Calculate the probability that the number plate selected begins with the letters AAA. I already know the total amount of possible combinations there are, do I just subtract the possibility of not getting three A's from 1?

• There is a problem of interpretation. Does a plate consist of $3$ letters and $3$ digits in any order, like 7C99XK, or is it $3$ letters followed* by $3$ digits? The answers will be different. – André Nicolas May 18 '13 at 7:57
• Eventual answers will probably be based on the 26 letters of the English alphabet. If you are working under a different assumption, you may want to comment on that or (may be preferrably!) modify the given answers to your setting. – Jyrki Lahtonen May 18 '13 at 8:06
• Hint: can you calculate the number of plates that do begin with AAA? I would think that is an easier question than the total number of plates! – Jyrki Lahtonen May 18 '13 at 8:08
• Great! You may consider posting your own solutions as an answer (I guess that there is a time limit or may be not - I don't know the rule). That way you get feedback on your answer, and, if correct, also upvotes :-). Welcome to the forum. Hope you stay. – Jyrki Lahtonen May 18 '13 at 8:47

I already know the total amount of possible combinations there are,
do I just subtract the possibility of not getting three A's from 1?


There are 26 x 26 x26 possible combinations of three characters from A-Z = 17,576

 Calculate the probability that the number plate selected
begins with the letters AAA


The probability is 1 in 17,576, or 5,689576695493855e-5

Btw, this implies that all letter combinations are issued equally. Some countries, for instance, do not issue the letter Q as it is easily confused with O. Also, some countries use the first one or two letters to indicate the city of issue, so some combinations may never occur (perhaps those containing an X or Z, etc, depending on country).

In fact, you can't really calculate the probability at all unless the question explicitly states that you are drawing a random plate form a pile which contains exactly one plate each of the complete sequence from AAA 1 to ZZZ 999.