The number of five digit numbers that are divisible by 6 which can be formed by choosing digits from $\{0,1…
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
648
540
1296
1080
Solution
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
$
\begin{aligned}
& =5 \times 6 \times 6 \times 2 \times 3 \\
& =1080
\end{aligned}
$
Hence, option (d) is correct