My club has 15 members. In how many ways can we choose a president, vice-president, secretary, and treasurer, if either the secretary or the treasurer must be elected vice-president and no other member can hold more than one office?
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---