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  4. The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 , is

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

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Solution:

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