A passcode for a certain security system consists of 2 letters, followed by 4 digits. If neither the letters or digits are allowed to repeat, how many different passcodes are possible?

Answer 1

I am assuming that there is no difference between UPPER case and lower case letters. If for example 'A' and 'a' are thought of as 2 different letters, then the number of possibilities will be much greater.

There are 26 letters in the English alphabet. The two letters can be chosen without repeating in 26*25 = 650 ways.

There are 10 digits between 0 and 9. Any four can be selected without repeating in 10*9*8*7 = 5040 ways.

The combination of a letters and 4 digits can be made in 650*5040 = 3,276,000 ways.

Answer 2

For letters there are 26 options to pick from. Since there are no repeats, that would decrease by 1 for each additional letter. For numbers is you can select 0-9, there are 10 possibilities. This would also decrease by 1 because no repeats are allowed. The number of possibilities for each digit are all multiplied together to to come up with the total number of options available.

(26)(25)(10)(9)(8)(7) = 3,276,000 passcodes