Q. 283.8( 25 Votes )

In a group of 50

Answer :

Given:


Total number of students = 50


Number of students studying English = 13


Number of students studying French = 17


Number of students studying Sanskrit = 15


Number of students studying English and French = 9


Number of students studying French and Sanskrit = 5


Number of students studying English and Sanskrit = 4


Number of students studying all three subjects = 3


Let U be the total number of students, E, F and S be the number of students passed in English, French and Sanskrit respectively



n(F S E) = a = 3


n(F S) = a + d = 5


3 + d = 5


d = 2


n(F E) = a + b = 9


3 + b = 9


b = 6


n(S E) = a + c = 4


3 + c = 4


c = 1


n(F) = e + d + a + b = 17


e + 2 + 3 + 6 = 17


e + 11 = 17


e = 6


n(E) = g + c + a + b = 13


g + 1 + 3 + 6 = 13


g + 10 = 13


g = 3


n(S) = f + c + a + d = 15


f + 1 + 3 + 2 = 15


f + 6 = 15


f = 9


(i) Number of students study French only = e = 6


(ii) Number of students study English only = g = 3


(iii) Number of students study Sanskrit only = f = 9


(iv) Number of students studying English and Sanskrit but not French = c = 1


(v) Number of students studying French and Sanskrit but not English = d = 2


(vi) Number of students studying French and English but not Sanskrit = b = 6


(vii) Number of students studying at least one of the three languages


= a + b + c + d + e + f + g


= 3 + 6 + 1 + 2 + 6 + 9 + 3


= 30


(viii) Number of students studying none of the three languages = Total – (a + b + c + d + e + f + g)


= 50 – (3 + 6 + 1 + 2 + 6 + 9 + 3)


= 50 – 30


= 20


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