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# Conditional probability

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407
3

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?

Sep 15, 2017

#3
+7606
+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.

Sep 15, 2017

#1
+18
+2

this hurts my brain, lol

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.

Sep 15, 2017
edited by Guest  Sep 15, 2017
#3
+7606
+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