What is the coefficient of d5e2c in (d+e+c)8

Name: What is the coefficient of d5e2c in (d+e+c)8
Uploaded: 2024-03-20T06:46:03.000Z
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Description: What is the coefficient of d5e2c in (d+e+c)8

Given (d+e+c)8 = (d+(e+c))8= Cr d8-r (e+c)r8= Cr d8-r Ck er-k ckr8= Cr Ck d8-r er-k ckr8 We need to…

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Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter12: Sequences, Series And Binomial Theorem

Section12.4: Binomial Theorem

Problem 12.78TI: Find the coefficient of the x4 term of (x+2)7.

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What is the coefficient of d⁵e²c in (d+e+c)⁸

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Step 1

Given

$\begin{array}{rcl} {(d + e + c)}^{8} & = & (d + {(e + c))}^{8} \\ = & {}^{8}{C_{r} d^{8 - r} {(e + c)}^{r}} \\ = & {}^{8}{C_{r} d^{8 - r} {}^{r}{C_{k} e^{r - k} c^{k}}} \\ = & {}^{8}{C_{r} {}^{r}{C_{k} d^{8 - r} e^{r - k} c^{k}}} \end{array}$

We need to evaluate coefficient of $d^{5} e^{2} c$

On comparing the coefficient , we get

$8 - r = 5 r = 8 - 5 r = 3 k = 1$

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