Question

The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$ , is_________

Answer 1

Answer: 514

Divisible by $2\to 450$
Divisible by $3\to 300$
Divisible by $7\to 128$
Divisible by $2$ & $7\to 64$
Divisible by $3$ & $7\to 43$
Divisible by $2$ & $3\to 150$
Divisible by $2,3$ & $7\to 21$
$\therefore$ Total numbers $=450+300-150-64-43+21=514$