A professor gives his students 7 essay questions to prepare for an exam. Only 5 of the questions will actually appear on the exam. How many different exams are possible?
Of the 5 questions, the first question can be chosen in 7 ways. Having chosen one question out of 7, the second question can be chosen in 6 ways, third question in 5 ways, the fourth question in 4 ways and the fifth question in 3 ways.
So the total number of ways of choosing 5 questions from 7 is
This can be generalized as follows:
Permutations: The number of ways of choosing