Question

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

• A. $216$
• B. $240$
• C. $600$
• D. $3125$

Answer 1

The correct option is A $216$

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 the 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 number formed $=120+96=216$.