Question

A counselor polled 144 students to see what classes that they wanted to take.
77 students chose Science
81 students chose English
84 students chose Math
38 students chose Science and English
36 students chose Science and Math
38 students chose English and Math
14 students chose Science, English and Math.
How many chose just science?

Answer 1

use a Venn diagram with 3 overlapping circles.
14 will be in the center where all 3 circles intersect
38 represents all students in area where English and math circles intersect
38-14 = 24
So only 24 chose only English and Math
get the idea...
try to fill in all the areas of all 3 circles

another way of doing it is
77 -38-36 +14
All students who picked science minus those who picked science and something else, but the 14 who picked all 3 will be double counted so thats why i added 14 as well.
= 17

Answer 2

With the same information how many chose math or English?

Answer 3

same thing
Math:
= 84 - 36 -38 + 14

English:
= 81 -38 -38 +14