Question

Five digit number divisible by $3$ is formed using $0,1,2,3,4,6$ and $7$ without repetition. Total number of such numbers are

• A. $720$
• B. $696$
• C. $642$
• D. $600$

Answer 1

Answer: (D)

$600$

$0,1,2,3,4,6$ and $7$

number should be divisible by $3$

If No. to be divisible by 3 the sum of digits should be divisible by 3

$\therefore$ cases will be

1,3,4,6,7=21 divisible so,$5!=120$

0,1,4,6,7=18 divisible so,$4\cdot 4!=96$

0,2,3,6,7=18 divisible so,$4\cdot 4!=96$

0,1,3,4,7=15 divisible so,$4\cdot 4!=96$

0,2,3,4,6=15 divisible so,$4\cdot 4!=96$

0,1,2,3,6=12 divisible so,$4\cdot 4!=96$

Therefore total = 600. Answer