Question

A survey conducted on $600$ students of $B.A$ part $I$ classes of a collage gave the following report. Out of $600$ students, $307$ took economics, $198$ took history, $230$ took sociology, $65$ took history and economics, $45$ took economics and sociology, $31$ took sociology and history and $10$ took all the three subjects. The report sounded very impressive, but the surveyor was fired. Why ?

Answer 1

Data are inconsistent since
$n(E\cup S\cup H)=n\left(E\right)+n\left(S\right)+n\left(H\right)-n(E\cap S)-n(S\cap H)-n(H\cap E)+n(E\cap S\cap H)$

$n(E\cup S\cup H)$=307+198+230-65-45-31+10=604