Permutation of #1-17 with no (interior and exterior) repetitions (in groups of 3)

Question

I want to make a list of permutations that includes the #'s 1-17 grouped in groups of 3, I do not care what order they come in, but I cannot have any 2 set of #'s repeat. Exp. 1,2,3 & 1,2,4 have the repeating 1,2. Is there anyone who can get me a list of the permutations of what they would be?

Answer 1

If you want arrangements of any three of the numbers in {1,2,...17}, that can be done in 17P3 ways; this number is 4,080. 

 

This would include outputs (in any order) such as {1,2,3}, {1,2,4} but you wish to exclude the second one because an earlier choice has already produced the 1,2.  A rather formidable task, this; I will be interested in seeing any other tutor replies. 

Answer 2

{1,2,3} U {4,5,6} U {7,8,9} U {10,11,12} U {13,14,15} U {16,17}