Excel is extremely poorly suited to this, but here is what you can do. Create a reference table that is 26x32. The first row is the letters of the alphabet. The rest of the table (31 cells below each letter) is all RAND().
Create a second table that is 20x31. The formula in cell A1 should be =INDEX(POSITIONS!$A$1:$Z$1,MATCH(LARGE(POSITIONS!$A2:$Z2,COLUMN()),POSITIONS!$A2:$Z2,0)).
Where POSITIONS!$A$1:$Z$1 are the letters and POSITIONS!$A2:$Z2 are the first row of random numbers. Copy this formula down and across, so every cell has a letter in it. None of the letters should repeat across the row.
Finally, create your 10x31 table. Creating the first row is a bit of a chore, since you must type CONCAT(LETTERS!A1, LETTERS!B1), then manually increment it (since just copying right would create overlapping pairs). After you finish that, you can copy down.