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?

Guest Sep 15, 2017

#3**+2 **

I think you must have 5 questions.

1! = 1 way to arrange 1 question

2! = 2 ways to arrange 2 questions.

3! = 6 ways to arrange 3 questions.

4! = 24 ways to arrange 4 questions.

5! = 120 ways to arrange 5 questions.

120 is more than 27. So there must be at least 5 questions on the quiz.

They could go in this order:

1, 2, 3, 4 ,5

1, 2, 3, 5, 4

1, 2, 4, 3, 5

1, 2, 4, 5, 3

1, 2, 5, 3, 4

1, 2, 5, 4, 3 ...etc.

hectictar Sep 15, 2017

#2**+2 **

Suppose the questions were numbered from: 1, 2, 3, 4, 5.........etc. In order for each of the 27 students to get the different order, or beginning with a different number, you would have to have a minimum of 5 questions in the puzzle. Anything less would have to be duplicated.

Guest Sep 15, 2017

edited by
Guest
Sep 15, 2017

#3**+2 **

Best Answer

I think you must have 5 questions.

1! = 1 way to arrange 1 question

2! = 2 ways to arrange 2 questions.

3! = 6 ways to arrange 3 questions.

4! = 24 ways to arrange 4 questions.

5! = 120 ways to arrange 5 questions.

120 is more than 27. So there must be at least 5 questions on the quiz.

They could go in this order:

1, 2, 3, 4 ,5

1, 2, 3, 5, 4

1, 2, 4, 3, 5

1, 2, 4, 5, 3

1, 2, 5, 3, 4

1, 2, 5, 4, 3 ...etc.

hectictar Sep 15, 2017