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So for this one I first used record ID to give each horse a numerical identifier, mainly to tell the difference between the two horses named Sally. Next was a formula tool just to join the ID number and the horses' name in the Horse column. Next was generate rows to list every position that every horse could finish in.
Cross tab was used so that every horse was listed in every position and then 4 text to column tools were used to parse out the horses so that every possible permutation was listed. A filter was used to to remove all entries that didn't make sense, for example a horse can't finish in first and third place.
A select tool was used to rename the columns and then loads of formula tools were used to remove the identifying numbers from each horse in each placing column.