Question

3. A multiple-choice test has 7 questions, with 4 possible answers for eachquestion. If a student were to guess the answer to each question, how manydifferent ways would there be to answer the test?

Answer 1

Each question can be answered in 4 ways.

For the first selection, we have 4 selections the student can make.

On the second selection, we will have

$\begin{gathered} 4\times4\text{ ways} \\ \Rightarrow4^2\text{ ways} \end{gathered}$

The third selection will have

$\begin{gathered} 4\times4\times4\text{ ways for selection} \\ \Rightarrow4^3\text{ ways} \end{gathered}$

If this goes on, this means that for n selections, the student will have

$4^n\text{ ways for selection.}$

The multiple-choice test in the question has 7 questions. That is

$4^7=16384$

This means that there would be 16,384 ways to answer the test.