A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is

Explanation

A number will be divisible by 3, if sum of the digits in number obe divisible by 3.
Here, 0+1+2+3+4+5=15, which is divisible by 3.
therefore, the digit that can be left out, while the sum still is multiple of 3, is either 0 or 3.
If 0 left out
Then, possible numbers=`.^(5)P_(5)=5!=120`
If 3 left out
Then, possible numbers=`.^(5)P_(5)-.^(4)P_(4)=5!-4!=120-24=96`
Hence, required total numbers=120+96=216