Question

Find the total number of ways of answering 5 objective – type questions, each question having 4 choices.

Answer 1

Hint: We will first start by finding the total ways in which we can answer a question. Then we will similarly find the ways in which the rest 4 questions can be done. Then we will use the fundamental principle of counting to find the total ways in which we can answer 5 objective – type questions.

Complete step-by-step answer:
Now, we have been given 5 objective type questions and each objective type question has 4 options.
Now, for the first question, we have four options and we can choose any one of them. So, we have 4 ways to answer 1 question.
Now, similarly for the 2nd question we have 4 options and so on. For all 5 questions we have four options.
Now, according to fundamental principle of counting the total ways in which we can answer 5 questions is,
$\begin{aligned} & 4\times 4\times 4\times 4\times 4 \\\ & ={{4}^{5}} \\\ & =1024 \\\ \end{aligned}$
So, the total ways of answering 5 questions are $1024$.

Note: To solve these types of questions it is important to note that we have used a fundamental principle of counting to count the total ways in this principle. We know that if one thing can be done in n ways and the other thing which can be done after, things can be done in m ways. So, the two things can be done in $m\times n$ ways.