Question

There are 19 students in a homeroom. How may different ways can they be chosen tobe elected President, Vice President, and Treasurer?

Answer 1

The number of students in a homeroom is

`n=19`

The number of posts to be chosen from is

`r=3`

Concept:

The above selection can be done using the permutation formula below

`^nP_r=(n!)/((n-r)!)`

By substituting the values, we will have

`\begin{gathered} ^nP_r=(n!)/((n-r)!) \\ ^(19)P_3=(19!)/((19-3)!) \\ ^(19)P_3=(19!)/(16!) \end{gathered}`

By expanding the factorial, we will have

`\begin{gathered} ^(19)P_3=(19!)/(16!) \\ ^(19)P_3=(19*18*17*16!)/(16!) \\ ^(19)P_3=19*18*17 \\ ^(19)P_3=5814\text{ ways} \end{gathered}`

Hence,

The final answer is = 5,814 ways