How many students took English and History, but not Math     ?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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A group of 422 students were surveyed about the courses they were taking at their college with the following results:

245 students said they were taking Math.
255 students said they were taking English.
139 students said they were taking History.
129 students said they were taking Math and English.
86 students said they were taking Math and History.
71 students said they were taking English and History.
32 students said they were taking all three courses.

How many students took English and History, but not Math     ? 

Expert Solution
Step 1

A group of 422 students were surveyed about the courses they were taking at their college

245 students said they were taking Math that is n(M) = 245
255 students said they were taking English that is n(E) =255
139 students said they were taking History that is n(H)=139
129 students said they were taking Math and English that is n(M and E) = 129
86 students said they were taking Math and History that is n(M and H) = 86
71 students said they were taking English and History that is n(E and H) = 71
32 students said they were taking all three courses that is n(M and E and H) = 32

 

now draw venn diagram

 

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