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)=$\frac{n!}{(n-r)!}$

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:

$P(35, 3)=\frac{35!}{(35-3)!}=\frac{35!}{(32)!}= \frac{35*34*33*32!}{32!}=35*34*33=39,270$


Answer: 39, 270