Answer to Question #332761 in Discrete Mathematics for op dot

Question

In a set vein, a certain examination, 72 candidates offered Maths, 64 offered English, 62 offered French, 18 offered both Maths and English, 24 offered Maths and French, and 20 offered English and French. While 8 candidates offered all the three subjects. How many candidates were there for the examination?

Answer 1

$$N(U)=N(M\cup E\cup F)$$

$$=N(M)+N(E)+N(F)-N(M\cap E)$$

$$-N(M\cap F)-N(E\cap F)+N(M\cap E\cap F)$$

$$=72+64+62-18-24-20+8=144$$

There were 144 candidates for the examination.