# How many exams consisting of three questions could a professor build from a bank of nine questions?

Nov 25, 2016

There are 504 possible exams the professor could build with 9 questions.

#### Explanation:

The professor has any one of 9 problems to select the first question from.

Once the first question is selected the professor then has 8 problems to select the second question from because 1 has already been selected.

Finally, for the third question the professor has 7 questions to select from because 2 have already been selected.

Therefore the number of possible different exams possible are:

$9 \cdot 8 \cdot 7 \implies 72 \cdot 7 \implies 504$