What is the coefficient of $x^{8} y^{5}$ $x^8 y^5$ in the expansion of ${(x + y)}^{13}$ $(x+y)^13$ ?

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Answer 1 · 2018-06-17T12:05:04

Coefficient of $x^{8} y^{5}$ $x^8 y^5$ is $1287$ $1287$

We know $(a+b)^n= nC_0 a^n*b^0 +nC_1 a^(n-1)*b^1 + nC_2 a^(n-2)*b^2+..........+nC_n a^(n-n)*b^n$

Here $a=x,b=y,n=13$ We know, $n C_r = (n!)/(r!*(n-r)!$

$x^8 *y^5$ will be in $6$ th term

$T_6= 13 C_5 * x^(13-5)* y^5= 13 C_5 x^8*y^5$

$13 C_5 =(13!)/(5!*(13-5)!) =1287$

Coefficient of $x^8 y^5$ is $1287$ [Ans]

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