In how many ways can 3 distinct numbers be chosen from the set {1,2,3,…,10} such that the sum of the numbers is odd?
You can choose them while sitting down, laying down, or standing up. So three ways.
(1, 2, 4) , (1, 2, 6) , (1, 2, 8) , (1, 2, 10) , (1, 3, 5) , (1, 3, 7) , (1, 3, 9) , (1, 4, 6) , (1, 4, 8) , (1, 4, 10) , (1, 5, 7) , (1, 5, 9) , (1, 6, 8) , (1, 6, 10) , (1, 7, 9) , (1, 8, 10) , (2, 3, 4) , (2, 3, 6) , (2, 3, 8) , (2, 3, 10) , (2, 4, 5) , (2, 4, 7) , (2, 4, 9) , (2, 5, 6) , (2, 5, 8) , (2, 5, 10) , (2, 6, 7) , (2, 6, 9) , (2, 7, 8) , (2, 7, 10) , (2, 8, 9) , (2, 9, 10) , (3, 4, 6) , (3, 4, 8) , (3, 4, 10) , (3, 5, 7) , (3, 5, 9) , (3, 6, 8) , (3, 6, 10) , (3, 7, 9) , (3, 8, 10) , (4, 5, 6) , (4, 5, 8) , (4, 5, 10) , (4, 6, 7) , (4, 6, 9) , (4, 7, 8) , (4, 7, 10) , (4, 8, 9) , (4, 9, 10) , (5, 6, 8) , (5, 6, 10) , (5, 7, 9) , (5, 8, 10) , (6, 7, 8) , (6, 7, 10) , (6, 8, 9) , (6, 9, 10) , (7, 8, 10) , (8, 9, 10) , Total = 60 distinct ways.
