Suppose 7 students are staying in a room of a hostel and they are allotted 7 beds placed one after another. Among them X does not want a bed next to Y, because he snores. Then, in how many ways,  can you allot the beds ?  

Considering $X$ and $Y$ to be allotted beds next to each other, the number of ways is $6 ! \times 2 !$. $\therefore$ Number of ways to allot the beds where $\mathrm{X}$ and $\mathrm{Y}$ are not next to each other $=7 !-6 ! \times 2 !=3600$