Find the number of 4 digit positive integers if the product of their digits is divisible by 3. Find the number of 4 digit positive integers if the product of their digits is divisible by 3.

Let $abcd$ be the required number.For the product of digits of this number is to be divisible by 3,atleast one digit has to be 3,6 or 9.
Total there are 9000 four digit numbers.
The possible combinations are 3 and three other digits,33 and two other digits,333 and one other digit,3333,6 and three other digits,66 and two other digits,666 and one other digit,6666,9 and three other digits,99 and two other digits,999 and one other digit,9999.
I dont know how to solve further.

How many have a digit product that is not divisble by $3$? You can then only use $6$ digits for all digits as also $0$ is forbidden for all digits. In total, as you said, there are $9000  =9\times 10^3$ $4$-digit numbers..
