Question

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4,5, 6 and 7 without repetition. Total number of such numbers are

• A. 312
• B. 3125
• C. 120
• D. 600

Answer 1

Answer: (D)

$0,1,2,3,4,6$ 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 $s0,4\cdot 4!=96$
$0,1,3,4,7=15$ 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 $4!=96$
Therefore total $=600$. Answer