Emma has decided to sign up for a new e-mail account. The program requires her to choose a password for the account that is first a letter, second a number digit, and finally a letter again (can be the same letter as the first entry). She has 26 letters and 10 digits to choose from. How many different passwords are possible?

26 * 10 * 26 = ?

The answer is 62

To find the number of different passwords that are possible, we need to consider the number of choices for each position in the password.

For the first letter, Emma has 26 letters to choose from since she can select any letter of the alphabet.

For the number digit, she has 10 digits (0-9) to choose from.

And for the final letter, she also has 26 letters to choose from.

To find the total number of passwords possible, we multiply the number of choices for each position:

26 (choices for the first letter) * 10 (choices for the number digit) * 26 (choices for the final letter) = 6,760.

Therefore, Emma has 6,760 different possible passwords to choose from.

To find the number of different passwords that Emma can choose, we need to calculate the possible combinations of a letter, a number digit, and a letter again.

First, we determine the number of choices for the first and third positions, which are both letters. Emma has 26 letters to choose from for each position. So, there are 26 choices for the first letter and 26 choices for the third letter.

Next, we determine the number of choices for the second position, which is a number digit. Emma has 10 digits (0-9) to choose from for this position.

To find the total number of different passwords, we multiply the number of choices for each position together:
Total number of different passwords = number of choices for 1st letter x number of choices for number digit x number of choices for 3rd letter

Total number of different passwords = 26 x 10 x 26

Calculating this expression gives us:
Total number of different passwords = 6,760

Therefore, Emma has 6,760 different possible passwords to choose from.