You have probably noticed some left-right symmetry in the triangular array. (If not, go notice it now.) Using choice notation, express this symmetry for a particular pair of entries in the triangular array. Pick three more symmetric pairs and use choice notation to express their symmetry. Can you now express the symmetry of the entire array using choice notation? Please attempt to do so. Using sugar-numbers, prove that this symmetry makes sense. (By the way, this is another example of combinatorial proof.)