1. A test contains 5 multiple-choice questions, each question has 4 choices. If Rachel answer all of the questions at random, in how many different...

There are 5 multiple-choice questions, each with 4 choices and we are asked the number of different ways to answer the questions.

We assume that each question is independent of the others as she is answering randomly. So we use the multiplication principle -- the number of different ways to perform a series of tasks is the product of the number of ways to perform each task.

Here there are 4 ways to answer each question, so we have 4*4*4*4*4 or `4^5=1024 ` different ways to answer the test.