SOLUTION: 6-letter codes are formed using the letters from the word 'EDUCATION' without any repetition. Find the number of different codes that begin with a vowel. Since there are 5 vowel

Question 760193: 6-letter codes are formed using the letters from the word 'EDUCATION' without any repetition. Find the number of different codes that begin with a vowel.
Since there are 5 vowel letters which are E, U, A, I and O, so there are 5 chances. Then, the remaining letters would have 8 choices for the remaining five.
So I wrote it like this: 5 x (8!/3!) and solving it would bring me with 33600. When I checked the textbook answer, it is 336000 which means I'm missing another zero. Now I'm not sure whether the textbook is wrong or I'm wrong, so can someone tell me the correct solution if my answer is wrong?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are correct.
there are 9 letters in the word EDUCATION
you have 5 choices for the first letter (EUAIO)
you have 8 remaining choices for the next 5 letters.
that would be 8P5 which is equal to 6720.
5 * 6720 = 33600.

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