Calculate the coefficient of x14,4 in the expansion of (x + y)18,

Question

asked Nov 15, 2021 48.9k views

1 Answer

Peakxu · Answer 1 · 2021-11-22T07:22:07+0000

Answer: 3060

Explanation:

Formula : (r+1)th term of
(a+b)^n :
$T_(r+1)=\ ^nC_r(a)^(n-r)(b)^r$

To find: Coefficient of
x^(14)y^4 in the expansion of
(x + y)^(18) .

Let the term in the expansion of
(x + y)^(18) be
^(18)C_r x^(18-r)y^r=x^(14)y^4

$\Rightarrow\ r=4$

Now, Coefficient =
^(18)C_r=^(18)C_4=(18!)/(4!14!) [
^nC_r=(n!)/(r!(n-r)!) ]

$=(18*17*16*15*14!)/(14!(24))\\\\=3060$

Hence, the coefficient of
x^(14)y^4 in the expansion of
(x + y)^(18) is 3060 .