How many five digit numbers divisible by $3$ can be formed using the digits $0,1,2,3,4,7$ and $8$ if each digit is to be used at most once?
The total number of $5$ digit numbers using the digits $0,1,2,3,4,7$ and $8$ is $6\times6\times5\times4\times3=2160.$
Now I found the numbers not divisible by $3$, i.e. even numbers ending in $2,4,8.$
Even numbers from the digits $0,1,2,3,4,7$ and $8$ are $5\times5\times4\times3\times3=930.$
So the numbers divisible by $3$ are $2160-930=1230$ but the answer is $744.$ Where I am wrong?