COT 3100 Quiz #1(Counting) Solutions Name : _______________________ 1/18/00 (Justify your answer to each question. In particular, state which counting rule you are using. If necessary, use the back of this page for your work.) 1) a) (4 pts) How many ways can a student answer a 10 question multiple choice test where there are four choices for each question? Answer : 4 10 Reason : You have 4 choices for each question. An answer to each question does not affect your choices for any other question. Thus, you can use the Product Rule and multiply 4x4. ..x4 to get the total possible number of ways to answer the test. b)(3 pts) What if the student MUST answer C exactly twice? Answer : ( 10 C 2 )3 8 . Reason : First pick where the 2 Cs must go. This can be done in ( 10 C 2 ) ways. For each of these choices, you can independently answer each of the other 8 questions with one of three answers, which can be done in a total of 3 8 ways. Since the choices of Cs and the rest of the answers are independent, apply the Product Rule. 2) (4 pts)
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