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?

JackWang778 Mar 23, 2020

#1**+2 **

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

CalTheGreat Mar 23, 2020