A new school randomly assigns a five-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, W, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?
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ok, well, each student gets five characters right, so the first character can be one of the nine possible characters
get me so far?
So you have 9 characters, and each student gets a 5 character code.
So suppose you have 5 boxes:
_ _ _ _ _
The first box can be filled with any of the 9 characters. Now you've used up that character. So since there are no repetitions, the 2nd box can be filled with any of the characters that are left.
So for the first box you have 9, then for the next one you used up one and now have 8, then you have used up two characters, so for the third one you have 7 characters left out of nine to use because you are not allowed repetitions.
If you were allowed repeating characters, you would have:
because for the first box you have 9, then for the next one you can pick whatever you want, so 9 again, etc.