Question

The coefficient of x⁸ y¹⁰ in the expansion of (x + y)¹⁸ is
(a) ¹⁸C₈
(b) ¹⁸p₁₀
(c) 2¹⁸
(d) none of these

Answer 1

(a) ¹⁸C₈

$$\begin{gathered} \mathrm{Suppose}\mathrm{the}(r+1)\mathrm{th}\mathrm{term}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{expansion}\mathrm{contains}{x}^8{y}^{10}. \\ \mathrm{Then},\mathrm{we}\mathrm{have} \\ {T}_{r+1}={}^{18}C_r{x}^{18-r}{y}^r \\ \mathrm{For}\mathrm{the}\mathrm{coefficient}\mathrm{of}{x}^8{y}^{10}\mathrm{We}\mathrm{have} \\ r=10 \\ \mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{coefficient}\mathrm{is}{}^{18}C_{10}\mathrm{or}{}^{18}C_8 \end{gathered}$$