permutation of 5 digit numbers divisible by 3 "The total number of possible combination of 5 digits numbers formed from the digits(0,1,2,3,4,5,6,7,8,9) which are divisible by 3?"
This was the question given to me by my mathematics teacher during out permutation and combination lessons;I was able to solve this with ease but later I was thought of modifing the problem a little bit to
"The total number of possible combination of 5 digits numbers formed from the digits(0,1,2,3,4,5,6,7,8,9) which are divisible by 3 without repetation of any digits?  eg 12345 not 33120"
I asked my teacher about the solution of the problem because i was unable to solve it with certain accuracy, he was unable to give me a satisfactory answer.
Can anyone help me in solving this problem
thank you.

There are in total $9*9*8*7*6$ 5 digit numbers with distinct digits.  The probability that a number is divisible by 3 in all these cases is $\frac {1}{3}$
Hence the number of numbers with 5 distinct digits satisfying the given conditions is 
$$9*9*8*7*6* \frac {1}{3}=9072$$
