Calculus and Above
Calculus Questions? Ask a Mathematician for Answers ASAP
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Here are the solutions:
Please feel free to ask if you have questions about any of these solutions.
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.