Question

Assume that the test has 15 questions, each with 6 choices for theanswer. An answer sheet has one answer for each question.How many different answer sheets are possible?

Answer 1

We can choose the correct answer for the 1st question any of 6 ways.

So that's 6 ways to choose the correct answer for the first question.

For each of the 6 ways we can choose the correct answer for the 1st question,

we can choose the correct answer to the 2nd question any of 6 ways.

So that's 6�6 or 36 ways to choose the correct answers for the first 2

questions.

For each of the 6�6 or 6� or 36 ways we choose the correct answer for the

1st 2 questions, we can choose the correct answer to the 3rd question any of 6

ways. So that's 6�6�6 or 6� or 216 ways to choose the correct answer for the

first 3 questions.

For each of the 6�6�6 or 6� or 216 ways we choose the correct answer for the

1st 3 questions, we can choose the correct answer to the 4th question any of 6

ways. So that's 6�6�6�6 or 6⁴or 1296 ways to choose the correct answer for the

first 4 questions.

etc., etc., and finally,

For each of the 6�6�6�6�6�6�6�6�6�6�6�6�6�6 or 614 ways we choose the correct

answer for the 1st 14 questions, we can choose the correct answer to the 15th

question any of 6 ways. So that's 6�6�6�6�6�6�6�6�6�6�6�6�6�6�6 or 615 ways to

choose the correct answer for the first 15 questions, which is all of them.

Answer 615 = 470184984576 ways.