If a password consists of 3 letters followed by 2 digits, how many different pas

If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using 26 letters and 10 digits?

If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using 26 letters and 10 digits?

Step 1: Understand that a password consists of 3 letters and 2 digits.
Step 2: Know that there are 26 letters in the English alphabet.
Step 3: For each of the 3 letter positions in the password, you can choose any of the 26 letters.
Step 4: Calculate the number of ways to choose the letters: 26 choices for the first letter, 26 for the second letter, and 26 for the third letter. This is 26 * 26 * 26, which is 26^3.
Step 5: Know that there are 10 digits (0-9) available for the digit positions.
Step 6: For each of the 2 digit positions in the password, you can choose any of the 10 digits.
Step 7: Calculate the number of ways to choose the digits: 10 choices for the first digit and 10 for the second digit. This is 10 * 10, which is 10^2.
Step 8: Combine the number of choices for letters and digits to find the total number of different passwords: Multiply 26^3 by 10^2.
Step 9: Calculate the final result: 26^3 * 10^2 = 17576000.

Combinatorial Counting – The question tests the ability to calculate the total number of combinations of letters and digits in a password format.
Exponential Growth – It assesses understanding of how to apply the rule of product in combinatorics, where the total combinations are the product of choices for each position.