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 $216$

Sum of all digits $=0+1+2+3+4+5=15$ which is divisible by $3$.

So, we need to remove one digit so that the sum remains divisible by 3.

a) Remove $0$: Number of ways $=5!=120$

b) Remove $3$: Number of ways $4\times 4\times 3\times 2\times 1=96$ ways.

Hence, the answer = $120+96=216$

Hence, $\left(a\right)$ is correct.