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

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6 sample questions

Question 1.
What is a combinatorial proof?
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Think about counting instead of algebra.
Question 2.
State Pascal's Identity.
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It relates binomial coefficients in a specific way.
3Question 3.
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)
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Remember, it involves choosing with or without a specific item.
4Question 4.
True or False: A combinatorial proof involves simplifying algebraic expressions.
- True
- False
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Think about what a counting argument means.
Question 5.
Using combinatorial proof, demonstrate that C(n, k-1) + C(n, k) = C(n+1, k).
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Think of including one extra item in the group.
Question 6.
Find the total number of ways to form teams of 4 from 10 members using Pascal's Identity.
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Consider the incremental selections through Pascal's layers.

4 more questions in this section. Enroll free to practise them all.