We know that the position of the vice president must be chosen by one of two already chosen.
For president, we have 15 possible opted, for the second position, vice president -
For secretary, we only have 14 options, since one was chosen for president, for the position vice president
For treasurer, we will have 13 options, and finally, 2 possible options for vice president, either the treasurer or the secretary,
The number of ways in which the committee can be chosen will be---
15*14*13*2=5460