Question

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

Answer 1

Answer: 3060

Step-by-step 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 = $^{18}C_r=^{18}C_4=\dfrac{18!}{4!14!}$     [$^nC_r=\dfrac{n!}{r!(n-r)!}$]

$=\dfrac{18\times17\times16\times15\times14!}{14!(24)}\\\\=3060$

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