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  • Find the coefficient of  in the expansion of <img alt="(a-b-c+d)^{10}" src="http

Find the coefficient of a^2 b^3 c^4 d in the expansion of (a-b-c+d)^{10}

Option: 1

12500


Option: 2

-12500


Option: 3

-12600


Option: 4

12600


Answers (1)

best_answer

\begin{aligned} & (a-b-c+d)^{10} \\ & =\sum_{r_1+r_2+r_3+r_4=10} \frac{(10) !}{r_{1} ! r_{2} ! r_{3} ! r_{4} !}(a)^{r_1}(-b)^{r_2}(-c)^{r_3}(d)^{r_4} \end{aligned}\\ \text{Now, we want to get} a^2 b^3 c^4 d \text{this implies that}\\ \begin{aligned} & r_1=2, r_2=3, r_3=4, r_4=1 \\ & \therefore \text { Coefficient of } a^2 b^3 c^4 d \text { is } \frac{(10) !}{2 ! 3 ! 4 ! 1 !}(-1)^3(-1)^4=-12600 \end{aligned}

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Sumit Saini

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