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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?

 Apr 10, 2020
 #2
avatar+111329 
+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

 

 

cool cool cool

 Apr 10, 2020

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