Question

In a survey of $500$ TV viewers, it was found that $285$ watch cricket, $195$ watch football and $115$ watch tennis. Also, $45$ watch both cricket and football, $70$ watch both cricket and tennis and $50$ watch football and tennis. If $50$ do not watch any game on TV, how many watch all the three games?

• A. $10$
• B. $20$
• C. $30$
• D. $15$

Answer 1

The correct option is B $20$

$n(A\cup B\cup C)=n\left(A\right)+n\left(B\right)+n\left(C\right)-n(A\cap C)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$
$450=285+195+115-45-50-70+n⟹n=20$