You need to have a password with 4
letters followed by 2
even digits between 0
and 9
, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your password?
There are 26 choices for the first letter of the password, as there are 26 letters in the alphabet.
For the second, third, and fourth letters, there are 25 choices remaining for each one after one letter has been used.
There are 5 choices for the first digit (0, 2, 4, 6, 8) and 5 choices for the second digit (0, 2, 4, 6, 8).
Therefore, the total number of choices for the password is:
26 * 25 * 25 * 25 * 5 * 5 = 812,500
So, there are 812,500 choices for the password with these criteria.