Status: Tags: #archivedCards/macm101/combinatorics Links: Combinatorics
The Binomial Theorem
Let x and y be variables, and let n be a nonnegative integer. Then $(x+y)^n$ =
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Prove (n / r) = (n / n-r)
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Prove
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Examples
Expand $(x+y)^4$
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Expand $(x+2y)^5$
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Determine coefficient of $x^9y^3$ in the expansion of $(2x-3y)^{12}$ ?
- Do combination trick on (12 3)
- Calculate coefficients from squared terms
- Multiply all together
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- Find equivalent binomial, then simplify the binomial
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Q9
9-
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10- Let X be an n-element set. Prove that there are 3 n ordered pairs (A, B) of subsets of X such that A ⊆ B ⊆ X.
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Created:: 2021-11-08 09:19