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?

sandwich Sep 11, 2023

#1**+1 **

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)

CPhill Sep 11, 2023