Chapter 10.5, Problem 37E

To determine

Tocalculate:

Total ways that you complete the exam.

Answer to Problem 37E

Total $45$ ways that you can complete the exam.

Explanation of Solution

Given information:

Total question of list: $10$

Answered questions: $8$

Formula used:

Expression for combination

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!\cdot r!}$

Where,

  $n=$ objects

  $r=$ time

Calculation:

As out of $10$ questions in an exam, $8$ questions have to be completed. The order of answering question is not main matter.

This shows that one can answer easy questions or questions in which anyone is comfortable most at the beginning followed by difficult ones.

So, now apply the combination. The expression of combination is as follows:

  ${}_n{C}_r=\frac{n!}{\left(n-r\right)!\cdot r!}$

As there are $10$ questions and $8$ questions you need to be answered. So, the required number of combinations is as follows:

  $\begin{array}{l}{}_{10}{C}_8=\frac{10!}{\left(10-8\right)!\cdot 8!}\\ =\frac{10!}{2!.8!}\\ =\frac{10\cdot 9\cdot 8!}{2\cdot 1\cdot 8!}\\ =45\end{array}$

Thus, the value of ${}_{10}{C}_8$ is $45$ .

Hence, there are $45$ ways that you can complete the exam.