A guidance counselor is planning schedules for 34 students. All students must take at least one of either Math, English, or History. 16 students say they want to take Math, 14 want to take English, and 15 want to take History. 5 say they want to take both English and History, and of these, 2 wanted to take Math as well. 8 want only History, and 10 want only math. How many students want only English

7 Students want only English

Step-by-step explanation:

Total Number of Students=34

n(students say they want to take Math)=16

n(students say they want to take English)=14

n(students say they want to take History)=15

n(both English and History)=5

Since 2 out of those who want to take English and History also wants Maths, The number of those who want the three subjects=2

n(who want only History)=8

n(who want only Maths)=10

This available information is placed on the Venn Diagram below.

n(H)=2+3+8+n(M∩H)

15=2+3+8+n(M∩H)

n(M∩H)=15-13=2

n(M)=10+2+2+n(M∩E)

16=10+2+2+n(M∩E)

n(M∩E)=16-14=2

n(E)=2+3+n(M∩E)+n(E only)

14=2+3+2+n(E only)

n(E only)=14-7=7