Question

18 guests have to be seated, half on each side of long table. 4 particular guests desire to sit on one particular side and 3 others on other side. The number of ways in which sitting arrangement can be made is –

• A. ¹¹C₉ ($\begin{matrix} 9 \end{matrix}$)²
• B. 2 × ($\begin{matrix} 9 \end{matrix}$)². ¹¹C₅
• C. ¹¹C₅.($\begin{matrix} 9 \end{matrix}$)²
• D. None of these

Answer 1

Answer: (C)

¹¹C₅.($\begin{matrix} 9 \end{matrix}$)²

Answer 2

$\frac { x ^ { 1 } , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } } { x _ { 1 } , \bar { x } _ { 2 } ^ { - } , - x _ { 3 } ^ { - } }$ (×,×,×, ....... ×)

⁹C₄×$\begin{matrix} 4 \end{matrix}$×⁹C₃×$\begin{matrix} 3 \end{matrix}$×$\begin{matrix} 11 \end{matrix}$ =$\frac{\begin{matrix} 9 \end{matrix}}{\begin{matrix} 4 \end{matrix}\begin{matrix} 5 \end{matrix}}$×$\frac{\begin{matrix} 9 \end{matrix}}{\begin{matrix} 3 \end{matrix}\begin{matrix} 6 \end{matrix}}$×$\begin{matrix} 4 \end{matrix}$×$\begin{matrix} 3 \end{matrix}$×$\begin{matrix} 11 \end{matrix}$

= ($\begin{matrix} 9 \end{matrix}$)² × ¹¹C₅