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Q. Number of four-digit positive integers if the product of their digits is divisible by $3$ is

Permutations and Combinations

Solution:

Product will be divisible by $3$ if atleast one digit is $0,3,6,9$
Now total four-digit no. $=9 \times 10^{3}$
Number of four-digit no. without $0,3,6,9=6^{4}$
Total number of four-digit integers $=9000-1296=7704$