Question: Using the English alphabet, how many 3-character case sensitive passwords are possible? There are…

Using the English alphabet, how many 3-character case sensitive passwords are possible? There are possible 3-character case sensitive passwords. (Type a whole number.)

Solution

To determine how many 3-character case-sensitive passwords are possible using the English alphabet, you need to consider both uppercase and lowercase letters. There are 26 letters in the English alphabet. Since it’s case-sensitive, there are 26 uppercase and 26 lowercase letters. This gives a total of \(26 + 26 = 52\) possible characters for each position in the password. Now, we calculate the number of possible passwords: Since each of the 3 positions in the password can be filled by any of the 52 characters: \[ 52 \times 52 \times 52 = 52^3 \] Calculating \(52^3\): \[ 52^3 = 52 \times 52 \times 52 = 140608 \] Therefore, there are 140608 possible 3-character case-sensitive passwords.