Number of ways to create a password 
You are allowed to choose from digits 0 to 9 (inclusive) and 20
  letters to make a password with 2 digits and 4 letters. You can repeat
  digits and letters in this password. How many different passwords are
  possible?

I know that there's $(10^2)(20^4)$ ways of selecting digits and numbers, but how do I account for the fact that digits and letters can go into different places in the password? Is it $\binom{6}{2}(10^2)(20^4)$?

There are you need to fill. Two spaces need to be filled with digits, so there are $6! \over 4!$ ways to arrange the two digits in six spaces. There are $4!$ ways to arrange the four letters in the four remaining spaces. There are $10^2$ ways to fill in the digit spots, and there are $20^4$ ways to fill in the letter spots. $(\frac{6!}{4!})(4!)(10^2)(20^4)$ is the number of possible passwords.
