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?
The test must contain at least 5 questions
To see why....4 questions can only be arranged in 4! = 4 * 3 * 2 * 1 = 24 different ways.......and this will not be enough.....no matter how she arranges the questions, some students will share the same arrangement
5 questions can be arranged in 5! = 5 * 4 * 3 * 2 * 1 = 120 different ways......and this will be more than enough