A professor gives his students 9 essay questions to prepare for an exam. Only 5 of the questions will actually appear on the exam. How many different exams are possible?

Answer 1

Since the order the questions are picked does not matter can use the difference factorial method.

The factorial of the number of available questions is divided by the factorial of the number of questions to be used and the factorial of difference between the number of question available and the number to be used.

possible out comes = 9!/(5!*4!)

The 5! cancels the 5, 4, 3, 2 and 1 of the 9!. This leaves 9*8*7*6/(4*3*2*1). This leaves 3*7*6.

Possible out comes = 126