How to calculate this permutation? How many ways can UNC, Duke and Florida State finish 1-2-3 in the AAC regular season rankings?
Please show work. Thank you. 

For lack of more information, we assume that the 1-2-3 ranking pertains to the three teams: UNC, Duke, and Florida State 
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: $$3\times 2\times 1 = 3!=6$$
