List questions from multinomial-theorem

47

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Find coefficient of $x^{10}$ in $\left(1−x^7\right) \left(1−x^8\right) \left(1−x^9\right) (1−x)^{-3}$

Published on 25 Mar 2026 - 11:16

151

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Multi Index Power Series

Published on 26 Apr 2026 - 5:30

426

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Coefficient of $x^i$ in $(x+x^2+...+x^k)^n$

Published on 25 Mar 2026 - 11:16

106

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Prove combinatorics equality?

Published on 16 Apr 2026 - 20:47

596

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Trinomial Theorem and Complex numbers

Published on 25 Mar 2026 - 14:19

78

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Trinomial Expansion and Complex Numbers

Published on 25 Mar 2026 - 11:08

105

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Prove $\frac{n !}{(n-k) !} \cdot k^{n-k}$

Published on 17 Apr 2026 - 12:15

185

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Multinomial - Sum of coeffecients with even powers

Published on 25 Mar 2026 - 12:49

654

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What are the chances that out of $n$ people playing rock, paper, scissors, only two choices are picked?

Published on 12 Apr 2026 - 17:00

476

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Product of a Multinomial done using Multinomial Theorem?

Published on 14 Apr 2026 - 10:44

152

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Is there a multinomial version of the DeMoivre-Laplace theorem?

Published on 14 Apr 2026 - 12:18

1.3k

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Is there a formula for the expansion coefficients of powers of an inner product?

Published on 12 Apr 2026 - 3:00

212

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The no. of positive integral solutions of the eqn. a×b×c×d×e=1050

Published on 25 Mar 2026 - 12:49

90

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No. of ways a candidate can qualify for an exam

Published on 25 Mar 2026 - 12:54

141

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Proving $\sum_{t=1}^j \sum_{r=1}^{t} (-1)^{r+t} \binom{j-1}{t-1} \binom{t-1}{r-1} f(r) = f(j)$

Published on 14 Apr 2026 - 18:22

List Question

Find coefficient of $x^{10}$ in $\left(1−x^7\right) \left(1−x^8\right) \left(1−x^9\right) (1−x)^{-3}$

Multi Index Power Series

Coefficient of $x^i$ in $(x+x^2+...+x^k)^n$

Prove combinatorics equality?

Trinomial Theorem and Complex numbers

Trinomial Expansion and Complex Numbers

Prove $\frac{n !}{(n-k) !} \cdot k^{n-k}$

Multinomial - Sum of coeffecients with even powers

What are the chances that out of $n$ people playing rock, paper, scissors, only two choices are picked?

Product of a Multinomial done using Multinomial Theorem?

Is there a multinomial version of the DeMoivre-Laplace theorem?

Is there a formula for the expansion coefficients of powers of an inner product?

The no. of positive integral solutions of the eqn. a×b×c×d×e=1050

No. of ways a candidate can qualify for an exam

Proving $\sum_{t=1}^j \sum_{r=1}^{t} (-1)^{r+t} \binom{j-1}{t-1} \binom{t-1}{r-1} f(r) = f(j)$

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