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

1 Answer
Binayaka C.
Jun 17, 2018

Coefficient of #x^8 y^5# is #1287#

Explanation:

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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