A mathcounts question The question is this.

There are $240$ pairs of numbers such as $(7,5318)$ or $(17,358)$ that can be formed using each of the digits $1$, $3$, $5$, $7$ and $8$ exactly once. What is the largest possible product of two such numbers?

Why wouldn't the answer be $87531 \times 87513$?
The answer key says $62333$.
This is a Mathcounts problem, from the $2011-2012$ handbook.

Start by realising that the answer must be one of the following:
8??? X 7
7??? X 8
8?? X 7?
7?? X 8?
These are all going to give a value greater than 56000.
Then consider how to replace the ???: must be with 531 in that order.
It’s less obvious what to do with the others. There are three possibilities for the single ? and then the ?? must be the other two digits in decreasing order.
So your candidates are:
8531 X 7
7532 X 8
853 X 71
851 X 73
831 X 75
753 X 81
751 X 83
731 X 85
