Pascal's identity states: C(n,k) = C(n-1,k-1) + C(n-1,k). Any combination value equals the sum of two values from the row above.
Intuition: to choose k items from n, either include the first item (choose k-1 from remaining n-1) or exclude it (choose k from remaining n-1).
Example: C(5,2) = C(4,1) + C(4,2) = 4 + 6 = 10. This identity is the foundation for building Pascal's Triangle.