If you are making passwords and they start with 2 letters from the alphabet and end with 3 digits from numbers 0 through 9 how many possibilities are there?

Answer 1

676,000 possibilities.

For case-sensitive passwords, it's 2,704,000 possibilities.

Passwords consist of 2 letters and 3 digits. That's 5 places. The first and second places can each hold 1 of 26 possibilities (26 letters), and positions 3, 4, and 5 can each hold 1 of 10 possibilities. The answer is 26 x 26 x 10 x 10 x 10 = 676000.

Maybe the passwords can be case-sensitive (i.e. an upper case letter is different from a lower-case letter), then there will be 52 possibilities for each letter - in each of the 1st and 2nd places. This gives the total as 52 * 52 * 10 * 10 * 10 = 2,704,000.

Note: An assumption we made is that the passwords are only 5 characters, consisting of 2 letters and 3 digits only. The question didn't say that no other characters are between these letters and numbers. If there are, then we don't have enough info to answer the question.