Question

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?

Answer 1

Counting techniques are used to make item selections, in this case we have three possible positions to choose from among the club members since the position of vice president must be chosen by one of two already chosen.

So, for the position of president we have 15 possible opted, for the second position, vice president - secretary, we only have 14 options, since one was chosen for president, for the position vice president - 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:

$C = 15 * 14 * 13 * 2 =5460$

Answer

The number of ways in which the described committee can be chosen is 5460