In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is

n(M)=23, n(P) = 24,  n(C)= 19n(M∩P)=12, n(M∩C)=9, n(P∩C)=7n(M∩P∩C)=4We have to find n(M∩P'∩C'), n(P∩M'∩C'),n(C∩M'∩P')Now n(M∩P'∩C')=n[M∩(P∪C)']=n(M)–n(M∩(P∪C))=n(M)-nM∩P∪M∩C=n(M)-N(M∩P)-n(M∩C)+n(M∩P∩C)=23-12-9+4=27-21=6n(P∩M'∩C')=n[P∩(M∪C)'] =n(P)–n[P∩(M∪C)]=n(P)-n(P∩M)∪(P∩C)  =n(P)-n(P∩M)-n(P∩C)+n(P∩M∩C)=24-12-7+4=9n(C∩M'∩P')=n(C)-n(C∩P)-n(C∩M)+n(C∩P∩M)=19-7-9+4=23-16=7