A computer password is required to be 7 characters long. How many passwords are possible if the password requires 3 letter(s) followed by 4 digits (numbers 0-9), where no repetition of any letter or digit is allowed

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Step-by-step explanation:

Note the requirements:

Because of that, permutation would be the most suitable way to count the number of possibilities.

There are ways to arrange three out of distinct letters (without replacement.)

Similarly, there are ways to arrange four out of distinct numbers (also without replacement.)

Therefore, there are possibilities for the three-letter section of this password, and possibilities for the four-digit section. What if these two parts are combined?

Consider: if the first three letters of the password were fixed, then there would be possibilities. However, if any of the first three letters was changed, the result would be another possibilities, all of which are different from the previous possibilities. These two three-letter sections along will give possibilities. Since there are three-letter sections like that, there would be possible passwords in total. That gives the number of possible passwords that satisfy these requirements.