Find the number of ways of choosing three different numbers from the set {1, 2, 3, ..., 12, 13, 14, 15}, so that their sum is 20.
(1, 4, 15) , (1, 5, 14) , (1, 6, 13) , (1, 7, 12) , (1, 8, 11) , (1, 9, 10) , (2, 3, 15) , (2, 4, 14) , (2, 5, 13) , (2, 6, 12) , (2, 7, 11) , (2, 8, 10) , (3, 4, 13) , (3, 5, 12) , (3, 6, 11) , (3, 7, 10) , (3, 8, 9) , (4, 5, 11) , (4, 6, 10) , (4, 7, 9) , (5, 6, 9) , (5, 7, 8) , Total = 22 such triplets
