Question

The number of $4$-digit numbers that can be formed using the digits $1,2,3,4,5$ that are divisible by $6$ when repetition is allowed.

Answer 1

If a $4$-digit number is formed by using the digits $1,2,3,4,5$ (repitition is allowed )

Thousands, Hundreds and Tens place can be filled up with $5$ ways each.

So, a total of $5\times 5\times 5$ ways to fill these three place.

Now, if the given numbers $1,2,3,4,5$ are filled in the unit place, they will form $5$ consecutive numbers, out of which only one is divisible by $6$.

So, total 4-digit numbers divisible by $6$ are $5\times 5\times 5\times 1=125$