Question

"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

Answer 1

Answer:

The exam can be answered with exactly 8 answers correct in 6435 ways.

Step-by-step explanation:

The order is not important.

For example, answering correctly the questions 1,2,3,4,5,6,7,8 is the same outcome as answering 2,1,3,4,5,6,7,8. So we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

Combinations of 8 questions from a set of 15. So

$C_{15,8} = \frac{15!}{8!(15-8)!} = 6435$

The exam can be answered with exactly 8 answers correct in 6435 ways.