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4 cards from this section. Quick, good the night before a test.
Define a combinatorial proof in your own words.
Think of it as proving something by counting.
State Pascal's Identity.
It's about combining combinations.
What does a combinatorial proof rely on?
It's all about how we count.
True or False: In a combinatorial proof, we simplistically expand both sides of an equation.
Recall the core concept of combinatorial proofs.
Using a combinatorial proof, verify the identity C(n, 2) + C(n, 1) = C(n+1, 2).
Consider two scenarios to illustrate the counting.
Prove via Pascal's Triangle properties that C(n+1, k) = C(n, k) + C(n, k-1) holds true recursively.
Visualize how each layer adds to the next in Pascal's Triangle!
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