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Katarina [22]
3 years ago
11

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 4 true false questions, Part B

consists of 6 multiple-choice questions with one correct answer out of five, and Part C consists of 5 multiple-choice questions with one correct answer out of six. How many different completed answer sheets are possible?
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
8 0

Answer:  374416

Step-by-step explanation:

Given : A test requires that you answer first Part A and then either Part B or Part C.

Part A consists of 4 true false questions, Part B consists of 6 multiple-choice questions with one correct answer out of five, and Part C consists of 5 multiple-choice questions with one correct answer out of six.

i.e. 2 ways to answer each question in Part A.

For 4 questions, Number of ways to answer Part A = 2^4

5 ways to answer each question in Part B.

For 6 questions, Number of ways to answer Part B = 5^6

6 ways to answer each question in Part C.

For 5 questions, Number of ways to answer Part C = 6^5

Now, the number of ways to  completed answer sheets are possible :_

2^4\times5^6+2^4\times6^5\\\\=2^4(5^6+6^5)\\\\=16(15625+7776)\\\\=16(23401)=374416

Hence, the number of ways to  completed answer sheets are possible = 374416

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