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

Step-by-step solution

The total possible 4 digit numbers are 9 × 10 × 10 × 10 = 9000 Let, X is the 4 digit number divisible by 3 1002 ,   1005 ,   … … … ,   9999 a = 1002 ,   d = 3   &   a n = 9999 9999 = 1002 + n 3 - 1 3 n 3 = 3000 Let, Y is the 4 digit numbers divisible by 7 1001 , 1008 ,   … … … ,   9996 a = 1001 ,   d = 7   &   a n = 9996 9996 = 1001 + n 7 - 1 7 n 7 = 1286 Now, 4 digit numbers divisible by both 3 and 7 1