We show that exact results (at all energy scales) can be obtained in double-scaled SYK, which is the usual SYK model with the number of fermions in the interaction scaling as \sqrt{N}. These include the calculation of the full four-point function. The analysis does not involve summations of Feynman diagrams, but rather uses combinatorial tools. These results are related in the appropriate limit to recent results on SYK and the Schwarzian theory.