Chapter 8, Problem 64CR

To determine

To find: The number of possible schedule that the student can create when choosing one course of the each subject.

Answer to Problem 64CR

The number of possible schedules that the student can create is 216.

Explanation of Solution

Given:

The given statement is that the student can choose from the four math courses, three economic courses, six English courses and three humanities courses.

Calculation:

Consider the number of possible schedule that the student can make from the offering is,

  ${}^4{C}_1{}^3{C}_1{}^6{C}_1{}^3{C}_1$

Then, expand the above equation with the formula ${}^n{C}_r=\frac{n!}{r!\left(n-r\right)!}$ .

  $\begin{array}{c}{}^4{C}_1{}^3{C}_1{}^6{C}_1{}^3{C}_1=\frac{4!}{3!1!}\cdot \frac{3!}{2!1!}.\frac{6!}{5!1!}\frac{3!}{1!2!}\\ =4\times 3\times 6\times 3\\ =216\end{array}$

Thus, the number of possible schedules that the student can create is 216.