A group of 2n students consisting of n boys and n girls are to be arranged in a row such that adjacent members are of opposite sex. The number of ways in which  this can be done is 

$$\begin{gathered} \mathrm{n} \mathrm{boys} \mathrm{can} \mathrm{be} \mathrm{arranged} \mathrm{in} \mathrm{odd} \mathrm{places} \mathrm{in} \mathrm{n}! \mathrm{ways} \\ \mathrm{and} \mathrm{n} \mathrm{girls} \mathrm{can} \mathrm{be} \mathrm{arranged} \mathrm{in} \mathrm{even} \mathrm{places} \mathrm{in} \mathrm{n}! \mathrm{ways} \\ \mathrm{Similarly} \mathrm{boys} \mathrm{in} \mathrm{even} \mathrm{and} \mathrm{girls} \mathrm{in} \mathrm{odd} \mathrm{places} \mathrm{can} \mathrm{be} \mathrm{arranged} \\ \mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{ways} \mathrm{of} \mathrm{arrangements}=\left(2\right)(\mathrm{n}!)(\mathrm{n}!)=2(\mathrm{n}!{)}^2\text{ ways. } \end{gathered}$$