Question

The number of $4$ digit numbers that can be formed using the digits $1,2,5,6,7$ without repetition and that are divisible by $3$ is

Answer 1

Number is divisible by $3$ if sum of digits is divisible by $3$
Now $1+2+5+6+7=21$
So to form a $4$ digit number without repetition from the given digits one digit which is a multiple of $3$ has to be excluded i.e. $6$
$\therefore 1+5+2+7=15$ is divisible by $3$
Using $1,5,2,7$ number of required $4$ digit numbers $=4!=24$