Question

Suppose your friend was addressing the following prompt: "3 freshmen, 5 sophomores, 4 juniors, and 2 seniors have been nominated to serve on a student advisory committee. How many different committees can be formed if the committee is to consist of three people from different classes?

Answer 1

To find the total number of different committees consisting of three people from different classes, we calculate the combinations from each class separately and then multiply them: 3 (freshmen) × 5 (sophomores) × (4 juniors + 2 seniors) resulting in 90 different committees.

Step-by-step explanation:

The question asks us to determine how many different committees we can form if the committee is to consist of three people from different classes, namely a freshman, a sophomore, and either a junior or a senior. Since we are selecting one person from each class without replacement, we use combinations to solve this.

First, we choose one freshman from the 3 available: there are 3 combinations for this selection. Next, we select one sophomore from the 5 available, yielding 5 combinations. Finally, we need to pick either a junior or a senior. We have two scenarios here:

• Selecting 1 junior from the 4 available: 4 combinations
• Selecting 1 senior from the 2 available: 2 combinations

Now, we add the number of ways to choose a junior or a senior: 4 (juniors) + 2 (seniors) = 6 combinations. To get the total number of different committees, we multiply the number of combinations from each class: 3 (freshmen) × 5 (sophomores) × 6 (juniors or seniors) = 90 different committees.