Difference between revisions of "Multinomial Theorem"
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== Proof == | == Proof == | ||
=== Using [[induction]] and the Binomial Theorem === | === Using [[induction]] and the Binomial Theorem === | ||
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=== Combinatorial proof === | === Combinatorial proof === | ||
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Revision as of 19:43, 17 February 2016
The Multinomial Theorem states that
where
is the multinomial coefficient
.
Note that this is a direct generalization of the Binomial Theorem: when it simplifies to
Contents
Proof
Using induction and the Binomial Theorem
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Combinatorial proof
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Problems
Intermediate
- The expression
is simplified by expanding it and combining like terms. How many terms are in the simplified expression?
(Source: 2006 AMC 12A Problem 24)
Olympiad
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This article is a stub. Help us out by expanding it.