Throw those darts #1

Harbo and Bela, two very happy pnomes, owned a carnival booth where players could win prizes playing games. One day they thought it might be a good idea to have two dart games to play in their booth.

Bela designed the first dart game. Its target board had three circles with the numbers 10, 20, and 40 in them.

The game was simple. A player threw three darts. The score was figured out by adding up the numbers in the circles where the darts hit. To plan for the prizes, Bela needed to know all of the different scores that were possible when all three darts hit the circles. She started doing some arithmetic in her head.