Question

The number of five digit numbers that are divisible by $6$ which can be formed by choosing digits from $\{0,1,2,3,4,5\}$, when repetition is allowed, is

• A. 648
• B. 540
• C. 1296
• D. 1080

Answer 1

Answer: (D)

If number is divisible by $6$, then it should be an even number and divisible by $3$ also, so sum of the digits should be divisible by $3.$
Now last digit can be fill by $0$ or $2$ or $4$ . First place can be filled by $5$ choices (except $0$ ) second and third can be filled by $6$ choices.
Now fourth place is filled such that it must be of form $3k$ or $3k+1$ or $3k+2$. So it can be fill by $2$ choices $(0$ or 3$)$ as whole number must be divisible by $3$ so, total numbers
$=5\times 6\times 6\times 2\times 3$
$=1080$