Exercise 1 Page 768

We want to determine in how many ways can a president, vice president, and secretary be randomly selected from a class of 25 people.

Since there are 25 students, we have 25 ways to choose the president.

Since the vice president cannot be the president, we have 25-1= 24 ways to choose the vice president.

Now, since 2 students have their roles chosen, there are 25-2= 23 ways to choose the secretary.

Next, recall that we can use the Fundamental Counting Principle to find the answer. In this case, the number of ways to choose 3 roles is the product of the number of ways to choose each of them. 25* 24* 23 Now, let's calculate this product. 25 * 24 * 23 = 13 800