Chapter 15.5, Problem 6WE

To determine

To calculate: The number of ways to form a 4 member committee.

Answer to Problem 6WE

The number of ways to select an form a four member committee are $120$ .

Explanation of Solution

Given information:

There are 5 seniors, 4 juniors, 3 sophomores and 2 freshmen in a student council as members.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that there are 5 seniors, 4 juniors, 3 sophomores and 2 freshmen in a student council as members.

To form a 4 member committee such that one member of each class must be there.

There are 5 ways to select a senior.

There are 4 ways to select a junior.

There are 3 ways to select a sophomore.

There are 2 ways to select a freshmen.

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $5\times 4\times 3\times 2=120$

Thus, the number of ways are $120$ .