Final answer:
To calculate the number of different passwords with a letter of the alphabet as the first entry, we consider the number of choices for the first letter and multiply it by the number of choices for the remaining characters. The total number of different passwords is 1,945,536.
Step-by-step explanation:
To calculate the number of different passwords that can be made if the first entry has to be a letter of the alphabet, we need to consider the number of choices for the first letter and multiply it by the number of choices for the remaining characters in the password.
There are 26 options for the first letter since there are 26 letters in the alphabet. For the remaining characters, we can use any combination of letters and/or numbers. Let's assume we have a password length of 4. There are 36 options (26 letters + 10 numbers) for each of the remaining three characters.
To find the total number of different passwords, we multiply the number of options for the first letter by the number of options for each of the remaining characters: 26 * 36 * 36 * 36 = 1,945,536.