# Enumeration question

• Oct 13th 2009, 04:16 PM
melody
Enumeration question
A group of university students are polled on their food preferences. Of the group, 35 liked pies, 54 liked pizza and 65 liked burgers. Fifteen of the students liked pies and burgers, 23 liked burgers and pizza, and 22 liked pies and pizza. There were 15 students who liked all three foods. If 110 students were polled, how many must have answered that they did not like any of the foods? please help me, thank you .
• Oct 13th 2009, 04:51 PM
Plato
Quote:

Originally Posted by melody
A group of university students are polled on their food preferences. Of the group, 35 liked pies, 54 liked pizza and 65 liked burgers. Fifteen of the students liked pies and burgers, 23 liked burgers and pizza, and 22 liked pies and pizza. There were 15 students who liked all three foods. If 110 students were polled, how many must have answered that they did not like any of the foods? please help me, thank you .

Do you know how to draw a Venn diagram with three circles and fill it in?
That is the crux of this question.
If you do not, please do a web-search for 'Venn diagrams'.
• Oct 13th 2009, 07:53 PM
melody
Quote:

Originally Posted by Plato
Do you know how to draw a Venn diagram with three circles and fill it in?
That is the crux of this question.
If you do not, please do a web-search for 'Venn diagrams'.

yes , I see, I have already draw the Venn diagram,this is my written, but seem not correct.
(35-15) + (54-15) + (65-15) = 109
(20-15) + (39-15) = 29
(50-23) + (39-23) = 43
(20-22) + (39-22) = 15
then, use 110 - 29 - 43 - 15 = 23
is this correct??
Is there any other easy way to do it??
• Oct 14th 2009, 07:34 PM
yoonsi
EDIT: I think I got it actually.

Well, what I did was:

22 - 15 = 7 Number of people who like pies and pizza but do not like burgers
23 - 15 = 8 etc...
15 - 15 = 0 etc...

54 - (7 + 15 + 8) = 24 Number of people who like Just pizza
35 - (7 + 15) = 13 etc...
65 - (8 + 15) = 42

Then just minused the sub total