Questions: Lewis High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each. Position People interested Faculty member Ms. Russell, Mr. Mitchell Male student Jose, Ryan, John, Chang Female student Linda, Mary, Jane, Jina Parent Mr. Watson, Dr. Cooper, Ms. Evans, Mrs. Walker, Mr. Morgan Based on this list, how many ways are there to fill the four committee positions?

Lewis High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each.
Position People interested
Faculty member Ms. Russell, Mr. Mitchell
Male student Jose, Ryan, John, Chang
Female student Linda, Mary, Jane, Jina
Parent Mr. Watson, Dr. Cooper, Ms. Evans, Mrs. Walker, Mr. Morgan

Based on this list, how many ways are there to fill the four committee positions?

Transcript text: Lewis High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each. \begin{tabular}{|c|l|} \hline Position & \multicolumn{1}{|c|}{ People interested } \\ \hline Faculty member & Ms. Russell, Mr. Mitchell \\ \hline Male student & Jose, Ryan, John, Chang \\ \hline Female student & Linda, Mary, Jane, Jina \\ \hline Parent & Mr. Watson, Dr. Cooper, Ms. Evans, Mrs. Walker, Mr. Morgan \\ \hline \end{tabular} Based on this list, how many ways are there to fill the four committee positions? $\square$

Solution

Solution Steps

Step 1: Understand the Problem

We are given a committee structure with a specific number of positions, each requiring one candidate. For each position, there is a set number of interested candidates. Our task is to calculate the total number of ways to fill all positions in the committee.

Step 2: Apply the Fundamental Counting Principle

The fundamental counting principle states that if there are $n_1$ ways to perform the first task, $n_2$ ways to perform the second task, and so on, up to $n_k$ ways to perform the $k$th task, then the total number of ways to perform all $k$ tasks in sequence is $n_1 \times n_2 \times ... \times n_k$.

Step 3: Calculate the Total Number of Ways

To calculate the total number of ways to fill the committee, we multiply the number of candidates interested in each position: $n_1 \times n_2 \times n_3 \times n_4$. Given our inputs, this calculation is $160$.