Question

Five digit number divisible by $3$ is formed using $0,1,3,4,6,7$ without repetition. Total number of such numbers are

• A. $312$
• B. $3125$
• C. $120$
• D. $7216$

Answer 1

Answer: (A)

A number is divisible by $3$ if sum of its digits be divisible by $3$.
Hence, the selection of $5$ digits for forming five digit numbers divisible by $3$
are either $1,3,4,6,7$ or $0,1,4,6,7$ or $0,1,3,4,7$. In first case i.e. when $1,3,4,6,7$ are taken as digits, the numbers of five digit numbers will be $5!=120$. In rest of the two cases, we have $4\times 4!=96$ in each case.
$\therefore$ Total number of required numbers
$=120+(2\times 96)=312$