There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms?

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room

So total number of ways of  choosing rooms

$$\begin{gathered} =7_{C_1}\times 6_{C_2}\times 4_{C_4} \\ =\frac{7!}{1!2!4!} \end{gathered}$$