Question

A teacher is making a multiple choice quiz. She wants to give each student the same questions, but have each student's questions appear in a different order. If there are twenty-seven students in the class, what is the least number of questions the quiz must contain?

Answer 1

If there is one question, the exam can have one unique order.

If there are two questions, the exam can have two different orders

If there are three questions, the exam can be arranged in 3*2 = 6 different orders

If there are four questions, the exam can be arranged in 4*3*2 = 24 different ways.

Then she needs five questions, which permit to order them in 5*4*3*2 =120 different ways.