My sister is playing a dart game at an arcade. She can earn 2, 3, or 6 points with each dart. She scored 24 points. How many ways could she score 24 points given that each dart thrown landed on the dart board?

Answer 1

2 & 3 are both factors of 6.
Meaning whenever 6 goes in a set, it can be replaced by two 3's or three 2's.

6 * 4
6 * 3; 3 * 2
6 * 3; 2 * 3
6 * 2; 3 * 4
6 * 2; 2 * 6
6 * 2; 3 * 2; 2 * 3
6 * 1; 3 * 6
6 * 1; 2 * 9
6 * 1; 3 * 4; 2 * 3
6 * 1; 3 * 2; 2 * 6
6 * 0; 3 * 8
6 * 0; 2 * 12
6 * 0; 3 * 6; 2 * 3
6 * 0; 3 * 4; 2 * 6
6 * 0; 3 * 2; 2 * 9

1 + 2 + 3 + 4 + 5 = 15 ways.