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------------------------------------------------ The letters F, G, H, J, and K are used to form 4-letter passwords for an office security system. How many different passwords can be formed if the letters can be used more than once in a password?

A) 625
B) 1024
C) 1025
D) 3125

To calculate the number of possible 4-letter passwords using the letters F, G, H, J, and K with repetition allowed, we use the counting principle to find 5^4 = 625 different combinations. Therefore, the answer is A) 625.

Explanation:

The question involves finding the number of 4-letter passwords that can be formed using the letters F, G, H, J, and K, where repetition of letters is allowed. Since there are 5 letters to choose from for each place in the password and there are 4 places, we can use the counting principle to calculate the total number of different passwords. This principle states that if we have multiple steps in a process and there are 'n' ways to perform the first step, 'm' ways to perform the second step, and so on, the total number of ways to perform the entire process is the product of the number of ways to perform each step.

In this case, for each of the 4 places in the password, we have 5 choices, which gives us 5 × 5 × 5 × 5 different combinations. Therefore, the number of different 4-letter passwords is: 54 = 625.

Thus, the correct answer is option A) 625.