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Finding the coefficient of $x^{10}$ in $(1+x^2-x^3)^8$

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#binomial-coefficients #multinomial-coefficients
1.4k
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Faster way to find coefficient of $x^N$ in $(1 + x + x^2 + x^3 + ... + x^A)^K$

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#combinatorics #binomial-coefficients #generating-functions #multinomial-coefficients
432
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Prove the Descartes' rule of signs

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#polynomials #roots #multinomial-coefficients
645
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Finding the coefficient of $x^m$ in $(x+x^2+x^3+.....+x^i)^n$

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#combinatorics #generating-functions #binomial-theorem #multinomial-coefficients
207
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max-weighted sums of multinomial coefficent

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#combinatorics #asymptotics #approximation #multinomial-coefficients #combinatorial-proofs
1k
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Help finding the expected value and variance of a multinomial distribution.

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#probability #statistics #conditional-expectation #variance #multinomial-coefficients
131
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What is the coefficient of $x^2$ in the polynomial..

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#combinatorics #polynomials #products #multinomial-coefficients
44
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Find the coefficientof $x^n$ in the expansion of $\frac{2-3{x}}{2x^2-3x+1}$

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#binomial-coefficients #multinomial-coefficients
465
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How to show that $\sum_{k} (-1)^k{{a+b}\choose{a+k}}{{b+c}\choose{b+k}}{{c+a}\choose{c+k}} = \frac{(a+b+c)!}{a!b!c!}$

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#combinatorics #summation #binomial-coefficients #factorial #multinomial-coefficients
728
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Distribution of blood types and alleles

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#probability #statistics #probability-distributions #multinomial-coefficients
689
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Distribution of distinguishable objects into indistinguishable groups & Stirling number

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#combinatorics #permutations #combinations #multinomial-coefficients
217
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Derivatives of exp(f(x)) and partitions of an set

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#combinatorics #derivatives #integer-partitions #multinomial-coefficients
699
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How to compute quintinomial coefficients?

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#combinatorics #binomial-coefficients #multinomial-coefficients #project-euler
78
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Coefficients of products of binomials

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#combinatorics #algebra-precalculus #multinomial-coefficients
687
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Dirichlet prior / Multinomial distribution / Posterior

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#probability #probability-distributions #bayes-theorem #multinomial-coefficients

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