Ninjutsu combinations are extremely simple because for the 2-part and 3-parts, it only matters what you ended with. The beginning 1/2 for 2/3-chain don't matter as long as they are different. 123 and 213 give the same thing.
Or to put it more simply, there are only 6 combinations (not counting the 1-part Shuriken), 1 is not worth remembering (Hyoton, lolbind), 3 are for single-target (Huton Suiton Raiton), and 2 (Doton/Katon) are situational for AoE. You don't really need to memorize all of them.