Suppose your license plate has three digits (between 0 and 9) followed by three letters (between A and Z). If a license number is selected randomly, what is the probability that yours is the one selected?

$\frac{1}{17 , 576 , 000}$

Explanation:

For each space, we have either a number (3 spaces with 10 choices in each) or a letter (3 spaces with 26 choices each). That means that there are:

${10}^{3} \times {26}^{3} = 17 , 576 , 000$ plates.

We have one plate in all of possibilities, and so the probability of having ours picked is:

$\frac{1}{17 , 576 , 000}$