permutation -number of numbers of four different digits formed from the digits of the number 12356 such that it is divisible by 4

Question

The number of numbers of four different digits that can be formed from the digits of the number 12356 such that it is divisible by 4??

Answer 1

Hint: If a number ends in $12$, $32$, $52$, $16$, $36$, $56$, it is multiple of $4$. How many ways can you fill the other two digits?

Answer 2

The answer to this is quite simple. Adding to what @ajotatxe has written, any number is divisible by $4$, if the last $2$ digits are multiples of $4$. From the given list the following are possible in the last $2$ places: $12, 16,32, 36,52, 56$. Hence $6$ ways.

Now, the remaining $2$ digits can be any of the $3$ digits from the list, as $2$ have been used up in the last $2$ places.

Therefore, the total number of ways is: $3 \times 2 \times 6 = 36$ total ways

Note: I have made the necessary edits to my answer. Apologies as I had mistaken the question... And a bunch of thanks to @Daniel Fischer