There are 17 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?
There are 17 options for the first position (President). After one student has been chosen, there are 16 options for the second position (Vice President). After two students have been chosen, there are 15 options for the third position (Treasurer). Finally, after three students have been chosen, there are 14 options for the fourth position (Secretary).
Therefore, the total number of different ways to choose the four positions is:
17 * 16 * 15 * 14 = 43,680 different ways. Answer: \boxed{43,680}.