Question

The coefficient of $x^8{y}^{10}$ in the expansion of $(x+y{)}^{18}$ is

• A. ${}^{18}{C}_8$
• B. ${}^{18}{P}_{10}$
• C. $2^{18}$
• D. None of these

Answer 1

The correct option is A

${}^{18}{C}_8$

${}^{18}{C}_8$

Suppose the (r+1)th term in the given expansion contains $x^8{y}^{10}$

Then, we have

$T_{r+1}={}^{18}{C}_r{x}^{18-r}{y}^r$

For the coefficient of $x^8{y}^{10}$ we have:

r=10

Hence, the required coefficient is ${}^{18}{C}_{10}or{}^{18}{C}_8$