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.