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? Could someone explain how to do this?

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? Could someone explain how to do this?

anonymous · Answer

suppose the quizzes have questions. then there are n! different ways to order the questions.  so you want an n with n! >27

brinazarski · Answer

Mhmm...

anonymous · Answer

$$4!=24$$ so you nee at least 5

brinazarski · Answer

So n = 5...?

hero · Answer

Wow that teacher has a lot of work to do.

brinazarski · Answer

Ikr Hero? XD

anonymous · Answer

yes you need at least 5 since 4!=24 and 5!=120

brinazarski · Answer

Okay, makes sense... any way I would know when you use n! > ? Idk, it never occurred to me to use that

hero · Answer

Wouldn't it be 
$$n! \ge 27$$