The summary of a survey of 100 students listed the following totals:
59 students did math homework
49 students did English homework
42 students did science homework
20 students did English and science homework
29 students did science and math homework
31 students did math and English homework
12 students did math, science and English homework
How many students did no math, no English and no science homework?
+128408 Let A = the number doing English homework
Let B be the number doing math homework
Let C be the number doing science homework
We can use this formula to find the number who took all three....100 - this = the number who took none of the courses
We have this
(A U B U C) = (A) + (B) + (C) - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)
(A U B U C) = 49 + 59 + 42 - 31 - 20 - 29 + 12 = 82
So....the number who took none of these courses = 100 - 82 = 18
