# Questions tagged [multinomial-theorem]

An extension to the binomial theorem. It gives the expansion of a multinomial $(x_0,\dots,x_{m-1})^n$.

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### Coefficient problem in algebra

Find the coefficient of $x^{8}$ in the expansion of $(1+x^2-x^3)^{9}$ I know the problem is simple if we use multinomial theorem and I got an answer $378$ using it. Can someone check it and ...
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### Trinomial expansion with power constraints

For the trinomial expansion $(a+b+c)^n$, I'd like to sum up the terms like $a^i b^j c^k$ with the constraint $i>j$. How to calculate it efficiently?
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### Finding sum multinomial

I did put x=$w, w^2 ,i ,-i$ but nothing of type is fetting formed. How come 1/2 is remaining constant. That means because of some substitution, $2a_o= a_1+ a_2$ is happening. Also tried putting x=ix.
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### Why can’t we use multinomial theorem here?

We have $10$ white, $9$ green and $7$ black balls. All balls are identical except for colour. While the solution for selecting number of ways in which one or more balls can be selected from these ...
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### A proving question based on binomial theorem [closed]

$$C_0-C1(a-1)(b-1)(c-1)_+C_2(a-2)(b-2)(c-2)+.... (-1)^nC_n(a-n)(b-n)(c-n)$$=0 I tried to solve this problem by using multinomial theorem but was not able to proceed further please help me out.
2answers
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### Weighted sum of product of binomial coefficients

I am trying to evaluate the sum $\displaystyle \sum_{n=1}^N \sum_{k=1}^n k\binom{n}{k} \binom{N-n}{k}x^k$, Here $x$ is some positive real My approach so far has been to first to compute the ...
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### Sum of coefficients in multinomial expansion

If $x,y,z$ are independent of each other, then the sum of the coefficients in the expansion of $(5x+3y-8z)^{30}$ is -
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