# Counting problem.

## Homework Statement

There are 285 math students. First homework was completed by 166 students, second by 148 and third by 129. First and second was completed by 108 students, first and third by 83 and second and third by 25 students. How many students have not completed at least one homework?

## The Attempt at a Solution

#### Attachments

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Principle of Inclusion-Exclusion would be useful here.

Gib Z
Homework Helper
Hmmm...well it looks like the answers at least one, because you haven't :p Im stumped

I can't see what your attempt at a solution is. However, the use of a Venn diagram would work well.

How annoying, I have put my Venn diagram on the picture yet it cannot be displayed. Anyway I get -25 + x for people who have just solved the first problem and 25 - x as the intersection of 2nd and 3rd homework. How can I get a negative value on the diagram? I get that 58 are missing a homework or 58 have completed all of the 3 homeworks. Do we need one extra data or is the trick in the negative number I get on the Venn diagram?

Last edited:

HallsofIvy
Homework Helper

Haki said:
How annoying, I have put my Venn diagram on the picture yet it cannot be displayed. Anyway I get -25 + x for people who have just solved the first problem and 25 - x as the intersection of 2nd and 3rd homework. How can I get a negative value on the diagram?
You appear to have "lost a sign". In your Venn diagram, you have let x be the (unknown) number of people who did all three asignments. Since 108 did the first and second assignments, yes, 108- x must have done ONLY the first and second. Since 83 people did the first and third assignments, yes, 83- x must have done ONLY the first and third. If you let y= the number of people who did only the first assignment, then y+ (108-x)+ (83- x)+ x= 166. That is, y+ 191- x= 166 so y= x- 25, NOT 25- x.

That is, y+ 191- x= 166 so y= x- 25, NOT 25- x.
I would know if my reasoning is correct. Who is yamini?

y = x - 25; by law of something y can be written as y = - 25 + x, take a look at my diagram I have it like that NOT like 25 + x.

Guess it only makes sense if the number is non-nengative, thefore 25 have completed all 3 homeworks for number of people who have done just homework 1 not to be negative and also the number of people who have done just 2nd and 3rd homework not be negative aswell. Therefore 33 people haven't done a single homework?

i m yamini here.the venn diagram is not getting enlarged,so for the sake of that i was asking you the answer and anyways i was not solving the sum using venn diagram,i was using some other method.so to know whether my answer is correct or not i have asked for answer and if u feel like i have done any mistake in asking answer then please say me..