how many cartag possibilities can you get from six characters with a space between the 1st and last 3.?

Question

My kids can ask for anyone's help on weekly "pow-wow's." The puzzle this week was the above question.
(000 AAA thru 999 ZZZ)
What is the # of possibilities. It is in the millions.

Answer 1

There are 10 digits and 26 letter choices. Assuming a pattern of 3 digits and then 3 letters, the number of possible combinations would be:

10 x 10 x 10 x 26 x 26 x 26 = 17,576,000

As others have mentioned, the DMV would probably disallow a few combinations that might be confusing (perhaps where 0 and O look alike), or series of plates where the three letters might imply an offensive word.

However, in terms of total possible combinations of plates with 3 numbers and 3 letters (in that exact order), the answer is 17,576,000 plates.

Incidentally the space between has no affect on the count since it is always in a fixed spot and doesn't contribute to making a different combination.

Answer 2

My daughters are 3 years and 3 months apart and I have always wished they were a little closer together. There is a 4 and a half year age difference between my second and third baby, but he is still too young to tell how their relationships are going to be. I think that about 2 years would be a good spacing but I've never had any that close together so not entirely sure.

Answer 3

This is how many different combinations are possible:

10 * 10 * 10 * 26 * 26 * 26

= 17,576,000

This is assuming that the numbers go ONLY on the left side, and letters go ONLY on the right side.

If both numbers AND letters can go on either side, then here is the number of possible combinations:

36 * 36 * 36 * 36 * 36 * 36

= 2,176,782,336

Answer 4

basically right, but there are some issues: like can they have either the letter O (oh) or the digit 0 (zero)? Or the letter I and the digit 1? So it might not be 36^6, it could be something smaller like 34^6.