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?

Question

agent47 · Answer

9*8*7*6*5 per student, but I'm not sure

terenzreignz · Answer

^I believe so

anonymous · Answer

huh

terenzreignz · Answer

Do you want to know the details? ;)

anonymous · Answer

yess

terenzreignz · Answer

ok, well, each student gets five characters right, so the first character can be one of the nine possible characters
get me so far?

agent47 · Answer

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.

agent47 · Answer

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.

agent47 · Answer

Thus:
9*8*7*6*5

agent47 · Answer

If you were allowed repeating characters, you would have:
9*9*9*9*9
because for the first box you have 9, then for the next one you can pick whatever you want, so 9 again, etc.