Question

In a class of $80$ students numbered $1$ to $80$, all odd numbered students opt for cricket, students whose numbers are divisible by $5$ opt for football and those whose numbers are divisible by $7$ opt for hockey. The number of students who do not opt any of the three games, is

• A. $13$
• B. $24$
• C. $28$
• D. $52$
• E. $67$

Answer 1

Answer: (C)

$28$

Here, $n\left(C\right)=40$, $n\left(F\right)=16$, $n\left(H\right)=11$, $n(C\cap F)=8$, $n(C\cap H)=6$, $n(F\cap H)=2$, $n(C\cap F\cap H)=1$
$\Rightarrow n(C\cup F\cup H)=40+16+11-8-6-2+1=52$
$\Rightarrow n(C^{{}^{\prime }}\cap F^{{}^{\prime }}\cap H^{{}^{\prime }})$
$=n\left(U\right)-n(C\cup F\cup H)$
$=80-52=28$