+1347 The summary of a survey of 500 students listed the following totals:
* 259 students did math homework
* 219 students did English homework
* 238 students did science homework
* 108 students did English and science homework
* 81 students did science and math homework
* 85 students did math and English homework
* 40 students did no homework
How many students did math, science, and English homework?
+128598 We will only be considering those who did some homework = 500 - 40 = 460
n ( M U E U S) =
n(M) + n(E) + n(S) - n (M ∩ E) - n(M ∩ S) - n(E ∩ S) + n (M ∩ E ∩ S)
460 = 259+ 219 + 238 - 85 - 81 - 108 + n (M ∩ E ∩ S)
460 = 442 + n (M ∩ E ∩ S)
460 - 442 = n (M ∩ E ∩ S)
18 = n (M ∩ E ∩ S)
