the question:

"a committee of three teachers are to select the winner from among ten students nominated for a special award. The teachers each make a list of their top three choices in order. The list have only one name in common, and that name has a different rank on each list. In how many ways could the teachers have made their lists?"

the answer is 3628800

i cant get that answer.. >.> as far as ive done it, there are 3 different lists, with 6 spots left unfilled. So i tried 3*(9permutate6) but thats not even close...