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

Since, a five digit number is formed by using digits $0,1,2,3,4$ and 5 , divisible by 3 i.e., only possible when sum of digits is multiple of three which gives two cases. Case I Using digits $0,1,2,4,5$ the number of ways $=4 \times 4 \times 3 \times 2 \times 1=96$. Case II Using digits 1, 2, 3, 4, 5 the number of ways $=5 \times 4 \times 3 \times 2 \times 1=120$ $\therefore$ Total numbers formed $=120+96=216$