Question

A quiz consists of 5 multiple-choice questions with 4 possible responses to each one. In how many different ways can the quiz be answered?

Answer 1

Think of it like this:

you have 4 objects (the 4 answer options, a, b, c, and d)

You are going to chose a group of 5, and the order matters (your answer to question #1 is independent of your choice on #3)

Repetition is allowed (you can answer "c" on all of the questions if you want to)

This is a simple permutation. Use the formula:

`\bold{n^r}`

where n is the number of objects (the number of answer choices)

and r is the number of objects you will choose (5, one answer for each question)

To solve:

`4^5`

`1,024 \longleftarrow` your answer!

Hope this helps! Feel free to ask any follow up questions, and please "vote up" :)

Answer 2

Answer: 1,024 different ways

Explanation:

We will use the Fundamental Counting Principle. There are 5 questions, each with 4 possible answers. To use the principle and answer the question, we will multiply 4 by itself 5 times.

4 * 4 * 4 * 4 * 4 = 1,024 different ways