Question

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?

Answer 1

Answer: 374416

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*5^6+2^4*6^5\\\\=2^4(5^6+6^5)\\\\=16(15625+7776)\\\\=16(23401)=374416`

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