Question 495815
<pre>
Assume that the test has 15 questions, each with 6 choices for the
answer.  An answer sheet has one answer for each question.

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 6² 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 6³ or 216 ways to choose the correct answer for the
first 3 questions.

For each of the 6·6·6 or 6³ 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 6&#8308;or 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 6<sup>14</sup> 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 6<sup>15</sup> ways to 
choose the correct answer for the first 15 questions, which is all of them.

Answer 6<sup>15</sup> = 470184984576 ways.

Edwin</pre>