A professor gives his students 9 essay questions to prepare for an exam. Only 4 of the questions will actually appear on the exam. How many different exams are possible?

Answer 1

so you are given 9 exam questions and 4 will actually be on the exam, so we will use a combination situation:

₉C₄ (if you have a calculator you can just solve it here, if not I'll show you how to solve by hand)

9!/(4!*(9-4)!)= 9*8*7*6*5!/(4!5!) (5! cancel and now we will expand the 4! and simplify)

9*8*7*6/(4*3*2*1) (4*2=8 so they cancel and 3 goes into 9 3 times so that simplifies more)

3*7*6/1=3*7*6=126 possible exams