Question

A test contains 10 true-false questions. To pass the test, there must be eight (8) or more correct answers.

1) In how many (different) ways can the test be filled out ?

2) In how many different ways can the test be filled out so that at least eight (8) answers or more are correct ?

Answer #1

Total 10 problems and each with two possible answers.

**a)** Total ways = 2^10 = 1024 ways because for
each question we can answer in 2 ways.

Hence, there are **1024** different ways to fill
out the test.

**b)** To pass we need 8 or more correct.

Total ways = 8 correct + 9 correct + 10 correct

= 45 + 10 + 1

= 56 ways.

Hence, total ways to pass the test is **56**.

Please comment if any doubt. Thank you.

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