Since there are three open offices, each with its own set of candidates, we can calculate the number of ways to fill each office separately and then multiply the results together using the multiplication principle.
For the first office, there are 14 candidates running. Therefore, there are 14 possible ways to fill the first office.
For the second office, after one candidate is selected for the first office, there are 13 candidates remaining. Therefore, there are 13 possible ways to fill the second office.
For the third office, after two candidates are selected for the first two offices, there are 12 candidates remaining. Therefore, there are 12 possible ways to fill the third office.
To find the total number of ways to fill all three offices, we multiply the number of ways to fill each office together using the multiplication principle:
Total number of ways = 14 x 13 x 12
Total number of ways = 2184
Therefore, there are 2184 different ways to fill the three open offices of president, treasurer, and secretary from a pool of 14 candidates.