I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Monday, September 20, 2010

License Plates

How many license plates are allowable by state law, if licence plate numbers have 3 letters folllowed by 4 digits? Keep in mind that the state restricts the number pattern 0000.

I think sadeesh is right, 175,760,000 - 1 is the answer I had. With at least 175 million possibilities, it's understandable why states don't have to worry about cutting out those undesirable phrases people come up with for their personalized license plates.

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1581840000 but my math is probably way out.

ReplyDeleteLetters = A,B,C....Z = 26

ReplyDeleteNumbers = 0,1,2....9 = 10

So the total no of combination will be

= 26 * 26 * 26 * 10 * 10 * 10 * 10

= 175760000

Since the combination 0000 is restricted, the total no of comb will be 175759999....

Just one per vehicle?

ReplyDeleteI think sadeesh is right, 175,760,000 - 1 is the answer I had. With at least 175 million possibilities, it's understandable why states don't have to worry about cutting out those undesirable phrases people come up with for their personalized license plates.

ReplyDeleteIs Sadeesh correct? By doing (26^3 x 10^4) - 1 you will only remove one of the combinations that contain 0000.

ReplyDeleteFor example, you may have removed AAA 0000, but you would still have AAB 0000, AAC 0000, etc.

Should the answer not be 26^3 x 9999 = 175,742,424?

You're right Anonymous. The number of combinations isn't down by 1. It's down by 26^3 * 1 (1 combination of 0000). So the answer is 175,742,424.

ReplyDeleteI even had this on a test once. You would think I could remember how it's done.