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(C) Let $M, P, B$ be the sets of students who failed in Mathematics,Physics,and Biology respectively. Let the regions in the Venn diagram be represent

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is $2$

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(C) Let $M, P, B$ be the sets of students who failed in Mathematics,Physics,and Biology respectively. Let the regions in the Venn diagram be represented by $a, b, c, d, e, f, g$ as shown,and $h$ be the number of students who passed in all subjects.Total students = $100$,so $a+b+c+d+e+f+g+h = 100$. Given $h = 1$,so $a+b+c+d+e+f+g = 99$.Given:$1) 	ext{ Failed in Mathematics: } a+b+d+e = 50$$2) 	ext{ Failed in Physics: } b+c+d+f = 45$$3) 	ext{ Failed in Biology: } d+e+f+g = 40$$4) 	ext{ Failed in exactly two subjects: } b+e+f = 32$Summing equations $(1), (2), (3)$:$(a+b+d+e) + (b+c+d+f) + (d+e+f+g) = 50 + 45 + 40 = 135$$(a+b+c+d+e+f+g) + (b+d+e+f) + d = 135$$99 + (b+e+f) + 2d = 135$$99 + 32 + 2d = 135$$131 + 2d = 135$$2d = 4 \implies d = 2$.Thus,the number of students failing in all three subjects is $2$.

There are $100$ students in a class. In an examination,$50$ of them failed in Mathematics,$45$ failed in Physics,$40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then,the number of students failing in all the three subjects is:

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