Let M, P and C denote the students studying Mathematics, Physics and ChemistryAnd \\\\(U\\\\) represents total studentsSo, \\\\(n(U) = 200\\\\),\\\\(n(M) = 120, n(P) = 90\\\\)\\\\(n(C)= 70, n(M \\cap P) = 40, n(P\\cap C)=30\\\\)\\\\(n(M \\cap C)=50, n(M\\cup P \\cup C)' = 20\\\\)\\\\(\ herefore n(M \\cup P \\cup C)' = n(U) - n(M\\cup P \\cup C)\\\\)\\\\(\\Rightarrow 20=200-n(M\\cup P \\cup C)\\\\)\\\\(\\Rightarrow n(M \\cup P \\cup C) = 180\\\\)\\\\(\\Rightarrow n(M \\cup P \\cup C) = n(M) + n(P) + n(C)\\\\)\\\\(-n(M\\cap P)-n(P\\cap C) - n(C\\cap M)+n(C\\cap M \\cap P)\\\\)\\\\(\ herefore 180 = 120 + 90+70-40-30-50+n(C\\cap M \\cap P)\\\\)\\\\(\\Rightarrow 180=280-120+n(C\\cap M \\cap P)\\\\)\\\\(\\Rightarrow n(P \\cap C \\cap M) = 300- 280 = 20\\\\)Hence, the number of students studying all three subjects is \\\\(20\\\\).