How to calculate this permutation? [duplicate]

How many ways can UNC, Duke and Florida State finish 1-2-3 in the AAC regular season rankings?

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marked as duplicate by Ross Millikan, David Mitra, Javier Álvarez, Gerry Myerson, Brett FrankelFeb 11 '13 at 23:00

Please, could you be more specific? – Sigur Feb 11 '13 at 22:34
Sorry thats all I have. The teacher didn't specify anything else – Shaily Feb 11 '13 at 22:35
But can not you explain by yourself? You should know the aim of the exercise before trying to solve it or even ask for help. – Sigur Feb 11 '13 at 22:36
I searched. I am sorry. Thank you. – Shaily Feb 11 '13 at 22:36

Here we compute number of permutations of three objects. There are three possible choices for first place; then there are only two possible choices left for second place (since one team must have finished first). Finally, we are left with only one choice for the third place (the one team that didn't place first or second). These choices are multiplied to compute the total number of possible rankings: $$3\times 2\times 1 = 3!=6$$
Your teacher is incorrect! There is no logic to an answer of "$9$"! – amWhy Feb 11 '13 at 23:05