How many five digit positive integers that are divisible by 3 can be formed using the digits 0, 1, 2, 3, 4 and 5, without any of the digits getting repeating?
my explanation: total number of permutations with 0, 1, 2, 3, 4 and 5 to have 5 digits = 6.5.4.3.2=720 (includes numbers with 0 at the beginning)
now let us find the numbers with zero at the beginning = 5.4.3.2=120
so total no of digits = 720 - 120 = 600
but this is not the answer? the correct answer is 216.
can somebody correct me whats wrong with my approach and suggest a better solution.