Question

A test requires that you answer either part A or part B. Part A consists of 7 true-false questions, and part B consists of 5 multiple-choice questions with one correct answer out of five. How many different completed answer sheets are possible?

Answer 1

The number of different completed answer sheets possible is 400,000.

Step-by-step explanation:

To find the number of different completed answer sheets, we need to determine the number of ways to choose either part A or part B, and then calculate the number of possible combinations for each part.

For part A, since there are 7 true-false questions, each with 2 choices (true or false), there are 2^7 = 128 possible answer combinations.

For part B, since there are 5 multiple-choice questions, each with 5 choices, there are 5^5 = 3125 possible answer combinations.

To calculate the total number of different completed answer sheets, we multiply the number of choices for part A (128) by the number of choices for part B (3125), giving us a total of 128 * 3125 = 400,000 possible answer sheets.

Answer 2

Answer: 3253

Step-by-step explanation:

Given : A test requires that you answer either part A or part B.

Part A consists of 7 true-false questions.

i.e. there are 2 choices to answer each question.

Now, the number of ways to answer Part A :
`2^7=128` (1)

Part B consists of 5 multiple-choice questions with one correct answer out of five.

i.e. there are 5 choices to answer each question.

Now, the number of ways to answer Part B :
`5^5=3125` (2)

Now, the number of different ways to completed answer sheets are possible=
`128+3125=3253` [Add (1) and (2) ]