Practice Category 1 Of Combinations (12.3.1) - Combinatorial Proofs - Discrete Mathematics - Vol 2
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Category 1 of Combinations

Practice - Category 1 of Combinations

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a combinatorial proof?

💡 Hint: Think about how we count objects.

Question 2 Easy

Give an example of a combinatorial identity.

💡 Hint: Consider how combinations link together.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the goal of a combinatorial proof?

To simplify expressions
To prove counts are equal
To expand formulas

💡 Hint: Remember that simplification is not involved!

Question 2

True or False: In combinatorial proofs, you often simplify the expressions involved.

True
False

💡 Hint: Focus on the nature of proofs we've discussed.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove \( C(n, k) = C(n, n-k) \) using a combinatorial proof technique. What are the two perspectives?

💡 Hint: Reflect upon how could view the same set in two different ways.

Challenge 2 Hard

Use Pascal's identity to demonstrate a relationship involving \( C(5, 3) \). What are the distinct cases?

💡 Hint: Consider the choices available based on including or excluding one specified element.

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