Question

Given three members of a group -- Alice, Bob, and Carol -- in how many ways can these three be chosen to be the three officers (president, secretary, and treasurer) of the group, assuming no person holds more than one job?

Answer 1

The three officers of the group can be chosen in 3 different ways.

Step-by-step explanation:

In this scenario, Alice, Bob, and Carol need to be chosen for the positions of president, secretary, and treasurer of the group. Since no person can hold more than one job, this is a problem of permutations.

To determine the number of ways these three can be chosen for the positions, we use the concept of permutations. The number of permutations can be calculated using the formula:

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

Here, n represents the total number of members (3 in this case) and r represents the number of positions to be filled (also 3 in this case).

Substituting the values into the formula, we get:

P(3, 3) = 3! / (3 - 3)! = 3! / 0! = 3!/1 = 3

Therefore, there are 3 ways these three members can be chosen to be the three officers of the group.