Without full calculation, ¹¹C₅ + ¹¹C₆ can be simplified to what?
The governing identity is Pascal's identity: ⁿCᵣ₋₁ + ⁿCᵣ = ⁿ⁺¹Cᵣ. In the given sum, ¹¹C₅ is the term with index r - 1 when r = 6, and ¹¹C₆ is the term with index r. Therefore their sum becomes ¹²C₆ without evaluating either combination. This makes option A correct. Option C, ¹²C₅, is not the direct form produced by the identity for these adjacent lower indices, although symmetry can relate some combination values after further reasoning. Options B and D do not follow from Pascal's identity and have incompatible upper indices.