Question

Suppose a youth organization wants to choose a president, vice-president and secretary for the upcoming year from its 35 person membership. In complete sentences, explain why this is a permutation. Determine how many different ways the youth board can be chosen.

Answer 1

P(n, r)=
`(n!)/((n-r)!)`

is the formula which gives the total number of permutations of r objects out of n.

A permutation means an arrangement in a list, be it horizontally, or vertically.

So there is a first place, a second and so on.

Example: a, b, c and a, c, b are 2 different permutations.


with these in mind:


the problem described is a permutation problem, because the order is important.

We do not only care whether a certain person is chosen among the 3, we also care what position he/she will hold.

The total number of permutations of 3 objects out of 35 is calculated by the formula:


`P(35, 3)=(35!)/((35-3)!)=(35!)/((32)!)= (35*34*33*32!)/(32!)=35*34*33=39,270`


Answer: 39, 270