Hi Adrian, thank you for quick response.

From your answer I understand that I was not very clear about my question.

Subsets[Subsets[Range[10], {2}], {5}] is not the answer because the first set is {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, in which "1" s are used more than once. The list elements should be used once and ordering is not important for the pairs.

Let me give 5 sample sets to clarify

{1,2},{3,4},{5,6},{7,8},{9,10} -- {1,3},{2,4},{5,6},{7,8},{9,10} -- {1,2},{3,5},{4,6},{7,8},{9,10} -- {1,2},{3,4},{5,6},{7,9},{8,10} -- {1,2},{3,4},{5,10},{7,8},{9,6} = {2,1},{3,4},{5,6},{7,8},{9,10}

In all these sets list members are used only once and all members are used. Do you think I can use partitions to generate all these sets?

By the way there are 945 = 9!! = 9 x 7 x 5 x 3 x 1 sets with this property. I know the number but I can not generate them in Mathematica.

Any suggestion?