If I am making a ten character long password, consisting of uppercase and lowercase letters, and at least one number, how many possibilities are there? When I calculated it I got: $(10*10)(62^9)=1.3537087e+18$
However, this seems awfully high and it doesn't seem like my equation takes into account position properly.
There are 52 lowercase and uppercase letters and 10 digits, for a total of 62 characters. Assuming characters can be repeated, that is a total of $62^{10}$ passwords. However, if you are going to require at least one number, you have to then subtract all of the combinations that include no numbers, of which there are $52^{10}$, so the correct number of passwords is $62^{10} - 52^{10}$.