(a) What is a permutation of r elements of a set? How many permutations are there of n objects taken r at a time?

(b) In how many different ways can a president, vice-president, and secretary be selected from a group of 15 students?

(a)

To explain:

The permutation of r elements of a set, and find number of permutation of n objects taken r at a time.

Approach:

A permutation of a set of object is an ordering of these objects. If the set has r objects, then there are r! permutations of the objects.

If a set has n objects, then the number of ways of ordering the r elements subset of the set is denoted P(n,r) and is called the number of permutation of n objects taken r at a time and given by,

P(n,r)=

(b)

To find:

The number of ways to choose president, vice-president, and secretary from a group of 15 students.