Question

a club has 27 members. how many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

Answer 1

There are 122,400 ways to choose a president, vice president, secretary, and treasurer of the club.

Step-by-step explanation:

In this problem, we need to determine the number of ways to choose a president, vice president, secretary, and treasurer of the club from a group of 27 members. We cannot have a person holding more than one office.

To solve this, we can use the concept of permutations. Since the order of selection matters (i.e., choosing a different person for each office), we will use the formula for permutations.

The number of ways to select a president, vice president, secretary, and treasurer is given by:

P(27, 4) = 27P4 = 27! / (27-4)! = 27! / 23!

Simplifying this expression, we get:

P(27, 4) = 27 * 26 * 25 * 24 = 122,400

Therefore, there are 122,400 ways to choose a president, vice president, secretary, and treasurer of the club.