How many five-letter codes can be made if no letter can be used twice? (There are 26 letters in the alphabet.)
There are 26 choices for the letter in the first position, 25 choices for the letter in the second position, 24 choices for the letter in the third position, 23 choices for the letter in the fourth position, and 22 choices for the letter in the fifth position. Therefore, the total number of five-letter codes that can be made without using the same letter twice is 26 × 25 × 24 × 23 × 22 = 789,360. Answer: \boxed{789,360}.
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There are 26 choices for the first letter, 25 choices for the second letter (as we cannot use the letter that was chosen for the first position), 24 choices for the third letter (due to the same reason), 23 choices for the fourth letter, and 22 choices for the fifth letter.
Using the counting principle, we multiply these choices together to get the total number of five-letter codes:
26 × 25 × 24 × 23 × 22 = 789,360
Therefore, there are 789,360 different five-letter codes that can be made without reusing any letter.