Answer:
There are 12 people who can be president.
For each of those choices, there are 11 VP candidates. That’s 11 twelve times, or 132.
For each of those132 possibilities, there are 10 Secretary options, so 1320.
Now there are 9 people remaining who might be selected as Treasurer. That’s 11,880 combinations.
It’s this high because, while no one can be in two positions, all the possible arrangements of each four need to be counted.
For example, if Angela, Bradley, Cara, and Davide are the four chosen, they can be in any of these arrangements:-
ABCD | BACD | CABD | DABC
ABDC | BADC | CADB | DACB
ACBD | BCAD | CBAD | DBAC
ACDB | BCDA | CBDA | DBCA
ADBC | BDAC | CDAB | DCAB
ADCB | BDCA | CDBA | DCBA
This is 24 times the normal condition for this sort of problem, where those 4 are interchangeable. In that case, often framed as a roll of some number of dice, there would be only “12 choose 4” combinations, for a total of 495.