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Here are the solutions:
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I'm sorry about that. The correct result is 6. It's the preceding notation that is incorrect. It should have been:
C(6, 5) = 6! / (5! * (6 - 5)!) = 6
You're welcome. Please don't hesitate to ask if you discover anything that doesn't seem right or is confusing.
In part a there are 4 possible choices that the student can select from for each of the 10 questions. The total number of ways that the student can list the answers is then 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^10.
In part b, the only combinations to be counted are the ones where the student selected an incorrect answer. Since only 1 of the 4 answers is correct, there are 3 "incorrect" choices that the student can select from. Like the above explanation, in this case the student then has (3 choices for the first answer)*(3 choices for the second answer)*(3 choices for the third answer)... The total number of ways that 10 incorrect answers can be listed is then 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 3^10.
You're quite welcome.