**Question:**

how many *pairs* $lbrace H_i, H_jrbrace$ of edge-disjoint Hamilton cycles are in the complete graph $K_n$ with $n$ vertices?

while I could find information to the maximal number of edge-disjoint Hamilton cycles in $K_n$ I was not able to find anything about the number of combinations $lbrace H_1,,dots,,H_hrbrace$, i.e. the number of ways to select $h$ edge-disjoint Hamilton cycles from $K_n$, specifically for $h=2$