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Coefficient of $y^3.x^6$ in $(1+x+y)^5 . (1+x)^7$?

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#binomial-coefficients #binomial-theorem
318
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Find the smallest number for which the number divides completely into 101

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#binomial-coefficients #divisibility
29
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Probability problem involving binomial formula.

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#probability #binomial-coefficients
229
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Power series with "shifted" central binomial coefficients

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#power-series #binomial-coefficients
59
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Sum similar to the binomial sum

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#summation #combinations #binomial-coefficients #binomial-theorem
42
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Looking for an easy proof that the binomial coefficient is bounded by $2^{n-1}$

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#binomial-coefficients
168
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Polynomial Division of a "Special" Polynomial

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#sequences-and-series #trigonometry #polynomials #binomial-coefficients
131
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could someone please give some geometric explanation about $(a+b)^4$?

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#geometry #polynomials #binomial-coefficients
117
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Reccurence Relation for columns of Pascal's triangle

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#combinatorics #recurrence-relations #binomial-coefficients
34
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Sum over factorials, proof: $\forall_{n,j\in\mathbb{N}}:n=\left(2j+2n+1\right)\sum_{r=1}^{n}f\left(n,j,r\right)$

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#summation #proof-writing #binomial-coefficients #factorial
41
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Ways of ordering for a distinctive pack of cards

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#combinatorics #combinations #binomial-coefficients
179
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Combinatorial reasoning behind Hypergeometric distribution

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#combinatorics #probability-distributions #binomial-coefficients
149
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How to prove a closed expression for $\int_0^{\infty } \left(\frac{1-e^{-q}}{q}\right)^n \, dq$?

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#convergence-divergence #definite-integrals #binomial-coefficients
2.2k
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Proving that the expectation of a binomial random variable is $np$

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#probability #binomial-coefficients #binomial-theorem
68
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Show that $\sum_{k=0}^{2n}(-1)^k \binom{2n}{k}^2 = (-1)^n\binom{2n}{n}$

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#elementary-number-theory #binomial-coefficients #binomial-theorem

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