A professor gives his students 8 essay questions to prepare for an exam. Only 3 of the questions will actually appear on the exam. How many different exams are possible? Show your work
To find the number of different exams possible, we need to determine the number of ways we can choose 3 questions out of the 8 given by the professor.
This can be calculated using the combination formula:
nCr = n! / r!(n-r)!
Where n = 8 (total number of questions) and r = 3 (number of questions to be chosen for the exam).
8C3 = 8! / 3!(8-3)!
= 8! / 3!5!
= (8 x 7 x 6) / (3 x 2 x 1)
= 56
Therefore, there are 56 different possible exams that can be created from the 8 essay questions given by the professor.