Chapter 9.1, Problem 36E

Solution

To calculate: The numbers of different ways in which the 8 questions can be selected by professor Indiana Jones if he gives 20 questions to his class and 8 out it will be answered in final exams.

The resultant answer is $125,970$ ways.

Given information:

Professor Indiana Jones gives 20 questions to his class and 8 out it will be answered in final exams.

Formula used: The number of combinations of n objects taken r at a time denoted by $C_{n_r}$ and given by $C_{n_r}=\frac{n!}{r!\left(n-r\right)!}$ .

Calculation:

There are total 20 questions out of which 8 have to be chosen. Then the expression for it will become: $C_{{20}_8}$

Rewrite the expression using the formula $C_{n_r}=\frac{n!}{r!\left(n-r\right)!}$ ,

  $\begin{array}{c}{C}_{{20}_8}=\frac{20!}{8!\left(20-8\right)!}\\ =\frac{20!}{8!12!}\end{array}$

Now expand the factorial,

  $\frac{20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\cdot 12!}{8!12!}=125,970$

Therefore, there are $125,970$ ways in 8 questions can be selected.