Question

Six boys and six girls sit along a line alternatively in $x$ ways and along a circle (again alternately in $y$ ways), then

• A. $x = y$
• B. $y = 12x$
• C. $x = 10y$
• D. $x = 12y$

Answer 1

Answer: (D)

$x = 12y$

Answer 2

Clearly $x =6!\times6!+6!\times6!=2\left(6 !\right)^{2}$ $y=5!\times6!$ $\therefore \frac{x}{y}=\frac{2\left(6!\right)^{2}}{5!\,6!}=\frac{2\left(6 !\right)}{5 !}=\frac{2\times6\left(5!\right)}{5!}=\frac{12}{1}$ $\therefore x=12 \,y$