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Solution using multinomial theorem raised to a negative power

score 97 · Answer 1 · 2026-03-25 09:32:18

97

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Solution using multinomial theorem raised to a negative power

Published on 25 Mar 2026 - 9:32

score 372 · Answer 2 · 2026-03-25 09:24:02

372

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Proof explanation related to multinomial coefficients

Published on 25 Mar 2026 - 9:24

score 130 · Answer 3 · 2026-03-25 09:27:04

130

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Prove that $\|\mathbf{T}^n\|^2=\sum_{|\alpha|=n}\frac{n!}{\alpha!}\|\mathbf{T}^{\alpha}\|^2.$

Published on 25 Mar 2026 - 9:27

score 71 · Answer 4 · 2026-03-25 09:25:19

71

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coefficients in the expansion of multivariable expression

Published on 25 Mar 2026 - 9:25

score 424 · Answer 5 · 2026-05-10 16:13:41

424

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An urn contains $4$ red balls, $6$ green balls and $8$ blue balls. Probability with versus without putting the balls back

Published on 10 May 2026 - 16:13

score 50 · Answer 6 · 2026-03-25 11:08:26

50

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Multinomials for negative integer powers.

Published on 25 Mar 2026 - 11:08

score 185 · Answer 7 · 2026-03-25 11:04:37

185

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How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

Published on 25 Mar 2026 - 11:04

score 101 · Answer 8 · 2026-04-01 15:45:22

101

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How many passwords with 8 characters have :

Published on 01 Apr 2026 - 15:45

score 224 · Answer 9 · 2026-03-25 09:25:20

224

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Unexpected proof that $\alpha!$ divides $k!$ if $\alpha_1 + \dots + \alpha_n = k$.

Published on 25 Mar 2026 - 9:25

score 82 · Answer 10 · 2026-03-25 06:22:11

82

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How to prove $\sum_{\alpha_1=0}^k \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha = \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha$

Published on 25 Mar 2026 - 6:22

score 104 · Answer 11 · 2026-03-25 06:17:35

104

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Evaluating a sum involving multinomial coefficient

Published on 25 Mar 2026 - 6:17

score 111 · Answer 12 · 2026-04-06 05:12:00

111

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Multinational Coefficient Difficulty

Published on 06 Apr 2026 - 5:12

score 34 · Answer 13 · 2026-03-25 09:29:51

34

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$\sum_{0\leqslant y \leqslant z \leqslant k \leqslant n} (\binom{n}{k}\binom{n-k}{z}\binom{n-k-z}{y})$ =?

Published on 25 Mar 2026 - 9:29

score 293 · Answer 14 · 2026-03-25 07:53:26

293

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The coefficient of $x^n$ in the expansion of $\frac{2-3x}{1-3x+2x^2}$ is?

Published on 25 Mar 2026 - 7:53

score 111 · Answer 15 · 2026-03-25 09:32:28

111

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Multinomial coefficient without replacement, marbles in a bag.

Published on 25 Mar 2026 - 9:32

List Question

Solution using multinomial theorem raised to a negative power

Proof explanation related to multinomial coefficients

Prove that $\|\mathbf{T}^n\|^2=\sum_{|\alpha|=n}\frac{n!}{\alpha!}\|\mathbf{T}^{\alpha}\|^2.$

coefficients in the expansion of multivariable expression

An urn contains $4$ red balls, $6$ green balls and $8$ blue balls. Probability with versus without putting the balls back

Multinomials for negative integer powers.

How can I find the coefficient of $x^6$ in $(1+x+\frac{x^2}{2})^{10}$ efficiently with combinatorics?

How many passwords with 8 characters have :

Unexpected proof that $\alpha!$ divides $k!$ if $\alpha_1 + \dots + \alpha_n = k$.

How to prove $\sum_{\alpha_1=0}^k \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha = \sum_{|\alpha|=k} \dfrac{k!}{\alpha!} a^\alpha$

Evaluating a sum involving multinomial coefficient

Multinational Coefficient Difficulty

$\sum_{0\leqslant y \leqslant z \leqslant k \leqslant n} (\binom{n}{k}\binom{n-k}{z}\binom{n-k-z}{y})$ =?

The coefficient of $x^n$ in the expansion of $\frac{2-3x}{1-3x+2x^2}$ is?

Multinomial coefficient without replacement, marbles in a bag.

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