12.2. Example Proof of Equality

Try these first

1. 1.

   What does LHS stand for in a combinatorial proof?

   Hint

   Think about the left side of an equation.

2. 2.

   What is the formula to compute B8(n, k)?

   Hint

   Recall the definition of combinations.

3. 3.

   What is a combinatorial proof primarily focused on?

   • Algebraic expansion
   • Counting arguments
   • Visual proofs

   Hint

   Recognize the core principle of counting!

4. 4.

   Is Pascal's identity related to combinatorics?

   • True
   • False

   Hint

   Consider its impact on combinatorial identities.

5. 5.

   Using a combinatorial proof, demonstrate that B8(n, r) + B8(n, r - 1) = B8(n + 1, r).

   Hint

   Consider all possible combinations and how they naturally relate.

6. 6.

   Apply combinatorial reasoning to show why B8(n, 0) is always 1.

   Hint

   Think about the meaning of choosing nothing from a set.