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?

Guest Apr 10, 2020

#2**+2 **

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

CPhill Apr 10, 2020