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.

total numbers=9000.If a number has at least one of digit as 0,3,6,9 then the product can be divisible by 3.So left digits are 1,2,4,5,7,8 i.e 6 digits.total numbers by these 6 digits are 6^4=1296.
so total numbers divisible by 3 are:
9000-1296=7704.
