How many distinct sums can be obtained by adding three different numbers from the set {3, 6, 9, ... ,27 , 30}?
There are 10 elements, so the answer is C(10,3) = 120.
~ never mind ~
The possible sums are all multiples of 3
(18, 21, 24 ......78, 81) =
(81 - 18) / 3 + 1 =
63/3 + 1 =
21 + 1 =
22 distinct sums
