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Solution using multinomial theorem raised to a negative power

score 96 · Answer 1 · 2026-03-23 22:10:35

96

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Solution using multinomial theorem raised to a negative power

Published on 23 Mar 2026 - 22:10

score 371 · Answer 2 · 2026-03-24 13:20:21

371

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Proof explanation related to multinomial coefficients

Published on 24 Mar 2026 - 13:20

score 129 · Answer 3 · 2026-03-23 17:37:53

129

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

Published on 23 Mar 2026 - 17:37

score 70 · Answer 4 · 2026-03-24 13:43:22

70

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coefficients in the expansion of multivariable expression

Published on 24 Mar 2026 - 13:43

score 422 · Answer 5 · 2026-03-23 18:42:44

422

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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 23 Mar 2026 - 18:42

score 49 · Answer 6 · 2026-03-24 07:15:29

49

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Multinomials for negative integer powers.

Published on 24 Mar 2026 - 7:15

score 183 · Answer 7 · 2026-03-23 23:36:25

183

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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 23 Mar 2026 - 23:36

score 99 · Answer 8 · 2026-03-23 22:53:28

99

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How many passwords with 8 characters have :

Published on 23 Mar 2026 - 22:53

score 223 · Answer 9 · 2026-03-24 13:00:16

223

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

Published on 24 Mar 2026 - 13:00

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 110 · Answer 12 · 2026-03-25 06:16:21

110

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Multinational Coefficient Difficulty

Published on 25 Mar 2026 - 6:16

score 33 · Answer 13 · 2026-03-23 18:32:32

33

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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 23 Mar 2026 - 18:32

score 292 · Answer 14 · 2026-03-24 07:27:45

292

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

Published on 24 Mar 2026 - 7:27

score 110 · Answer 15 · 2026-03-23 17:33:08

110

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Multinomial coefficient without replacement, marbles in a bag.

Published on 23 Mar 2026 - 17:33

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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