## 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.

#### 6 comments:

1. 1581840000 but my math is probably way out.

2. Letters = A,B,C....Z = 26
Numbers = 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....

3. Just one per vehicle?

4. 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.

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

For 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?

6. 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.

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

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