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A great solution also!
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Let's say you have five dots in a line and another five dots in a line some distance away.
The total number of ways of drawing five lines, connecting the dots on one side with the dots on the other and each line connecting two dots that aren't connected by any other lines, will give the total number of ways of selecting the two questions, but we can't have the lines going straight across because that would be equivalent to selecting the same question for the same student.
Here's an equation using the inclusion-exclusion principle:
48,120 represents the total number of ways of drawing the five lines with at least one line going straight across.
That isn't what we want. We want the total number of ways of drawing five lines with none going straight across. So...
Last edited by Fruityloop (2016-04-10 17:09:44)
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Very well!
Let's say you have five dots in a line and another five dots in a line some distance away.
The total number of ways of drawing five lines, connecting the dots on one side with the dots on the other and each line connecting two dots that aren't connected by any other lines, will give the total number of ways of selecting the two questions, but we can't have the lines going straight across because that would be equivalent to selecting the same question for the same student.
Here's an equation using the inclusion-exclusion principle:48,120 represents the total number of ways of drawing the five lines with at least one line going straight across.
That isn't what we want. We want the total number of ways of drawing five lines with none going straight across. So...
Since each two questions for each student can be selected in two different ways we divide by 2^5.
I'm not sure exactly why my earlier answer was wrong.
Anyways, good job anonimnystefy! This is a hard problem.
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