Thank you for reporting, we will resolve it shortly
Q.
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
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 $3\, k$ or $3\, k+1$ or $3\, k+2$. 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 $
$=1080$