Question

In how many different ways can you answer a multiple choice test that has 5 questions and 3 choices for each answer?

Type a numerical answer in the space provided. Do not type spaces in your answer.

Answer 1

243

Explanation:

If there is one question that has three choices a1, a2, and a3, then there will be 3 i.e. 3¹ different ways of answering which are a1 or a2 or a3.

If there are two questions that have answer choices a1, a2, a3 and b1, b2, b3 then there will be 9 i.e. 3² different ways of answering which are a1-b1, a1-b2, a1-b3, a2-b1, a2-b2, a2-b3, a3-b1, a3-b2, and a3-b3.

Similarly, when there are 5 questions that have three choices each, then there will be 3⁵ i.e. 243 ways of answering options. (Answer)