How do I calculate permutations where some values are restricted? I am curious about the formula for determining the number of combinations there are in a given set where some values are restricted to a certain range. For example, if I have a 10 character, alphanumeric identifier where the first and last  character must be an uppercase letter, [A-Z] and the second and next to last character must be a number between 0 and 9. [0-9]. The six characters in the middle can be any alphanumeric character. 
I know that if I wanted to calculate the number of combinations with no restrictions that I would use the following formula:
x = (36 ^ 10)

However, I'm not sure how to calculate for the number, but this is where I'm heading:
x = (36 ^ 10) - (26 ^ 2) - (10 ^ 2)

Still, this doesn't feel right. Can you help me out?
 A: You multiply the number of choices at each position, so with two positions with $26$ choices, two with $10$ choices, and six with $36$
A: Unless I've misunderstood what you've wrote you could work out the permutations by multiplying the the number of possible values for each place holder together. For example with 10 place holders where each one had 36 possible values you simply do $36\times36\times...$ or $36^{10}$. 
For the situation you said you have the first place holder (or character) as a capital letter therefore we have 26 possible values, we then multiply that by the number of possible values for the next character which you want as values between 0-9, or 10 possible values. So we multiply $26$ and $10$ to give the total number the number of permutations for the two characters. We then continue this process by multiplying by the number of possible values for the next character (which is alphanumeric and therefore has 36 possibilities). Thus extending this to all 10 characters gives:
$$ 26\times 10\times 36^6 \times 10 \times 26$$
