There is a test with 10 questions. Each question has a choice of three answers, but only one answer is correct. How many ways are there to fill out the test?

By the way, we are learning combinations and permutations

3 choices for each of 10 questions is clearly 3^10

Naturally, there is only 1 way of getting all the answers right.

If, however, you want to know the order of questions to answer, then there are 10! ways to select the questions.

Rather a poorly worded question.

To find the number of ways to fill out the test, we need to consider the number of choices for each question and the total number of questions.

Each question has 3 choices, meaning there are 3 options for each of the 10 questions. Since each question is independent of the others, we can multiply the number of choices for each question together to find the total number of ways to fill out the test.

Using the multiplication principle, we multiply the number of choices for each question:

3 choices * 3 choices * 3 choices * ... * 3 choices (repeated 10 times)

So, the total number of ways to fill out the test is:

3^10 = 59,049 ways.

Therefore, there are 59,049 ways to fill out the test.