List questions from binomial-coefficients

Published on 19 Sep 2014 - 5:12

381

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What is the coefficient of$ x^6y^1$ in the expansion of $(3x^2+y)^4$?

Published on 28 Mar 2026 - 22:29

1.5k

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What is the coefficient of $x^4y^3z^3$ in the expansion of $(5x+1y+5z)^{10}$?

Published on 28 Mar 2026 - 22:29

168

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Binomial coefficients and order of infinity

Published on 20 Sep 2014 - 9:44

1.6k

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A urine test, the VMA test

Published on 20 Sep 2014 - 15:35

176

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The sum of binomial coefficients up to $k\le n/3$ does not exceed the $k$th coefficient

Published on 20 Sep 2014 - 19:48

260

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Question about ${n+1\choose k} = {n\choose k} + {n\choose k-1}$ proof?

Published on 20 Sep 2014 - 21:17

601

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How many ways can the school choose a President Vice President?

Published on 28 Mar 2026 - 22:28

67

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Find the values of a and b such that $\binom{2n}{2} = a\binom{n}{2} + b(n^2)$

Published on 21 Sep 2014 - 7:36

1.1k

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Placing m books on n shelves

Published on 21 Sep 2014 - 9:15

502

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Sums of binomial coefficients

Published on 21 Sep 2014 - 10:05

744

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Proving $\sum_i \binom{k}{k-i} \binom{n-k}{i} = \binom{n}{k}$

Published on 21 Sep 2014 - 13:40

378

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Prove $\sum_{i=0}^{i=x} {x \choose i} {y+i \choose x}+\sum_{i=0}^{i=x} {x \choose i} {y+1+i \choose x}$

Published on 21 Sep 2014 - 21:10

123

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Problem proving $ \sum_{r=0}^{n-1} \binom{2n-1}{r} = 2^{2n-2} $

Published on 22 Sep 2014 - 17:42

186

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Combinatorial approach to a binomial sum identity?

Published on 23 Sep 2014 - 3:49

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What is the coefficient of$ x^6y^1$ in the expansion of $(3x^2+y)^4$?

What is the coefficient of $x^4y^3z^3$ in the expansion of $(5x+1y+5z)^{10}$?

Binomial coefficients and order of infinity

A urine test, the VMA test

The sum of binomial coefficients up to $k\le n/3$ does not exceed the $k$th coefficient

Question about ${n+1\choose k} = {n\choose k} + {n\choose k-1}$ proof?

How many ways can the school choose a President Vice President?

Find the values of a and b such that $\binom{2n}{2} = a\binom{n}{2} + b(n^2)$

Placing m books on n shelves

Sums of binomial coefficients

Proving $\sum_i \binom{k}{k-i} \binom{n-k}{i} = \binom{n}{k}$

Prove $\sum_{i=0}^{i=x} {x \choose i} {y+i \choose x}+\sum_{i=0}^{i=x} {x \choose i} {y+1+i \choose x}$

Problem proving $ \sum_{r=0}^{n-1} \binom{2n-1}{r} = 2^{2n-2} $

Combinatorial approach to a binomial sum identity?

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