Question

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

Answer 1

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]