Question

The number of numbers divisible by 3 that can be formed by four different even digits is

• A. 18
• B. 36
• C. 0
• D. none of these

Answer 1

Answer: (B)

36

The even digits are $0,2,4,6,8$
Since we know that for divisibility by $3$ we just have to check that the sum of digits of the number is divisible by $3$.
4 digit number divisible by 3.=combination of $(2,4,6,0),(8,4,6,0)$
Hence the no. of such digits =$\{4!-3!\}+\{4!-3!\}=36$
We are subtracting $3!$ because if $0$ comes in the 1st place the number will no longer remain $4$ digit number.
Hence, option 'B' is correct.