Of a total of 100 students 28 study English 8 - English and German 10- English and French 5- French and German 3 students - all three languages.How many study only one language? How many not even one language
Answers
Given : Of a total of 100 students 28 study English 8 - English and German 10- English and French 5- French and German 3 students - all three languages.
To find : Number of Students Studying only one language or not even language
Solution:
Total Students = 100
Study English 28
English and German = 8 E ∩ G
English and French = 10 E ∩ F
French and German = 5 G ∩ F
all three languages = 3 E ∩ G ∩ F
Study more than one langugae
= (E ∩ G - E ∩ G ∩ F) + ( E ∩ F - E ∩ G ∩ F) + ( G ∩ F - E ∩ G ∩ F) + E ∩ G ∩ F
= ( 8 - 3) + (10 - 3) + ( 5 - 3) + 3
= 5 + 7 + 2 + 3
= 17
Number of Students Studying only one language or not even language = Total Studentrs - Students studying more than one language
= 100 - 17
= 83
83 Students Study only one or not even one
Studying english only = E - E ∩ G - E ∩ F + E ∩ G ∩ F
= 28 - 8 - 10 + 3
= 13
13 Students Studying English only
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