Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Fill in and evaluate a binomial-coefficient symmetry equality
Problem
Use binomial-coefficient symmetry to rewrite and evaluate \(C(8,2)\).
Big Picture
What this problem is really about
Combination symmetry comes from describing the same split in two complementary ways. Selecting k objects to include automatically determines the n minus k objects left out, so the counts match within the same row. Find the complementary lower index first, then evaluate whichever side requires fewer factors.
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