Why it is so hard to win even you got a 3D?

Imagine the 1st prize contain 348.

Before, the draw someone already given you "348" as the winning 3D. You might be thinking it is very easy to win since you only need to add 0-9 to 348. This way, it very wrong. 

If you think again.

The number can be:

3480
3481
3482
...
3489

And for each number, there are 24 permutations.

So in the end, what you get is

10*24 = 240 possible numbers to buy.

As each number like 3480 there are 24 permutations (3480, 4380, 8340...)

240 numbers is just too many numbers to buy if you think about it.

Imagine each number you buy $1 big, and you already need $240.

Hence, if there is a 4D number for it instead of 3D. Unless you are buying system roll which is 348R which is very expensive as well.