Hi. I am having difficulty with a word problem and hope someone can help. There has to be a simpler way than manually writing out each possibility.

"Kyle, Jim and Dan can't decide what sport they will play in school during recess the following day. On a slip of paper, each person writes a 1, 2, or 3 and puts the paper in a hat. The papers are then totaled. If the sum is 3, 4, or 5, all will play football. If the sum is 6 or 7, all will play basketball. If the sum is 8 or 9, all will play soccer. What sport will be played most often and why?"

Thanks in advance. I know that there are 27 different possibilities...