P(n, r)=[tex] \frac{n!}{(n-r)!} [/tex]
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:
[tex]P(35, 3)=\frac{35!}{(35-3)!}=\frac{35!}{(32)!}= \frac{35*34*33*32!}{32!}=35*34*33=39,270[/tex]
Answer: 39, 270
