In a certain school, there are 180 pupils in Year 7. One hundred and
ten pupils study French, 88 study German and 65 study Indonesian.
Forty pupils study both French and German, 38 study German and
Indonesian, and 26 study both French and Indonesian, while 19 study
German only. Find the number of pupils who study:
a all three languages b Indonesian only
c none of the languages d at least one language
e either one or two of the three languages.
Answers
Given :
total 180 pupils
Study French = 110
Study German = 88
Study Indonesian = 65
Study French and German = 40
Study German and Indonesian = 38
Study French and Indonesian = 26
Study German only = 19
To Find : number of pupils who study:
a all three languages
b Indonesian only
c none of the languages
d at least one language
e either one or two of the three languages.
Solution:
Study German only = G - F∩G - G∩I + F∩G ∩I
=> 19 = 88 - 40 - 38 + F∩G ∩I
=> F∩G ∩I = 9
Study all three languages = 9
Total = F + G + I - F∩G - F∩I - G∩I + F∩G ∩I + None
180 = 110 + 88 + 65 - 40 - 38 - 26 + 9 + None
=> None = 12
None of the Language = 12
Indonesian only = I - F∩I - G∩I + F∩G ∩I
=> Indonesian only = 65 - 38 - 26 + 9
=> Indonesian only = 10
at least one language = Total - None = 180 - 12 = 168
either one or two of the three languages. = Total - F∩G ∩I - None
= 180 - 9 - 12
= 159
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