Question

The 8 digits 0 through 7 are to be arranged in a 2x4 table (a table with 2 rows and 4 columns). How many ways are there to do this if for each column, the entry in row 1 must be less than the entry in row 2?

Answer 1

This is interesting... give me a moment.

Answer 2

I think this leads to factorials, but I'll need to sleep before I can figure out how. For now, I'll just say I've tested it on 1x2 and 2x2 tables and it has been (n+1)! where n is the number of columns.