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

Question

Number of four-digit positive integers if the product of their digits is divisible by 3 is (A) 2700 (B) 5464 (C) 6628 (D) 7704

Tardigrade Admin · Accepted Answer

Product will be divisible by 3 if atleast one digit is 0,3,6,9 Now total four-digit no. =9 × 103 Number of four-digit no. without 0,3,6,9=64 Total number of four-digit integers =9000-1296=7704

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

2700

5464

6628

7704

Product will be divisible by $3$ if atleast one digit is $0, 3, 6, 9$
Now total four-digit no. $= 9 \times 1 0^{3}$
Number of four-digit no. without $0, 3, 6, 9 = 6^{4}$
Total number of four-digit integers $= 9000 - 1296 = 7704$

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