Practice Pascal's Identity (12.3) - Combinatorial Proofs - Discrete Mathematics - Vol 2
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Pascal's Identity

Practice - Pascal's Identity

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a combinatorial proof?

💡 Hint: Think about counting instead of algebra.

Question 2 Easy

State Pascal's Identity.

💡 Hint: It relates binomial coefficients in a specific way.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Pascal's Identity state?

C(n
k) = C(n - 1
k) + C(n - 1
k - 1)
C(n
k) = C(n + 1
k) - C(n - 1
k)
C(n
k) = C(n
n - k)

💡 Hint: Remember, it involves choosing with or without a specific item.

Question 2

True or False: A combinatorial proof involves simplifying algebraic expressions.

True
False

💡 Hint: Think about what a counting argument means.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using combinatorial proof, demonstrate that C(n, k-1) + C(n, k) = C(n+1, k).

💡 Hint: Think of including one extra item in the group.

Challenge 2 Hard

Find the total number of ways to form teams of 4 from 10 members using Pascal's Identity.

💡 Hint: Consider the incremental selections through Pascal's layers.

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Reference links

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