Question

Find the number of numbers from $1$ to $1000$ are divisible by $60$ but not by $24$.

Answer 1

Let $n\left(A\right)=$ number divisible by $60=(60,120,...,960)=16$
$n\left(B\right)=$ number divisible by $24=(24,48,....,984)=41$
$n(A\cap B)=$ number divisible by both
$=120,240,....960=8$

Hence, number of numbers from $1$ to $1000$ are divisible by $60$ but not by $24$

$=n\left(A\right)-n(A\cap B)=16-8=8$.