Question

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

Answer 1

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 .