The number of 4 -digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.
 

Answers (5)

Total no of 4 digit numbers =9000\\

Divisible by  7=\left [ \frac{9000}{7} \right ]=1285\\

Divisible by  3=\left [ \frac{9000}{3} \right ]=3000\\

divisible by both 3 & 7 \Rightarrow \\ divisible by  21=\left [ \frac{9000}{21} \right ]=428\\

From inclusion exclusion principle,

numbers which are either multiple of 7 or 3

=9000-3000-1285+428\\

=5143

5143

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