Question

Referring to the given Venn diagram, the number of total students, who took History or Mathematics or Science, is:

• A. $183$
• B. $190$
• C. $148$
• D. $430$

Answer 1

The correct option is A $183$

The required set of students is denoted by regions lying inside the circles representing History or Mathematics or Science.

Let $H,M$ and $S$ denote History, Mathematics and Science respectively

$n\left(H\right)$ represents no. of students who took History

Same for maths and Science

Then, no. of students who took History or Mathematics or Science is given by

$n(H\cup M\cup S)=n\left(H\right)+n\left(M\right)+n\left(S\right)-n(H\cap M)-n(M\cap S)-n(S\cap H)+n(H\cap M\cap S)$

$=111+102+119-65-66-56+38=183$

Hence, option A is correct.