+0  
 
-1
23
1
avatar+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?

 Sep 11, 2023
 #1
avatar+129690 
+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)

 

cool cool cool

 Sep 11, 2023

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