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?
+9481 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.
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.
+9481 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.
