Question

Solve the following permutation: The student body of 40 students wants to elect a president, vice-president, secretary and treasurer.

Answer 1

Step-by-step explanation

In the question, we are given that the number of students in the class is 40 and there are namely four positions to be filled namely president, vice-president, secretary, and treasurer.

Steps

First, choose the president: You have 40 options. Then choose the VP: Since one person is already serving as president, you have 39 options for VP. for Secretary there are 38 options, and for treasurer 37. We will then multiply those four numbers or apply the permutation below.

`\begin{gathered} \\ \text{ }^(40)P_4\text{ =}(40!)/((40-4)!)=(40!)/(36!)=(40*39*38*37*36!)/(36!)=40*39*38*37=2,193,360 \end{gathered}`

Answer:2193360