A shopkeeper sells three varieties of perfumes and he has a large number of bottles 

of the same size of each variety in his stock. There are 5 places in a row in his showcase. 

The number of different ways of displaying the three varieties of perfumes 

in the show case, is

We have the following possibilities:

Number of selections                                               Number of Arrangements

$\begin{array}{r}{ }^3{C}_1{\times }^2{C}_2\\ { }^3{C}_2{\times }^1{C}_1\end{array}$                                                          $\begin{array}{r}{ }^3{C}_1{\times }^2{C}_2\times \frac{5!}{3!}=60\\ { }^3{C}_2{+}^1{C}_1\times \frac{5!}{2!2!}=90\end{array}$

Three bottles of one type and two distinct. Two bottles of one type, two bottles of second_ type and one from the remaining. Hence, required number of ways e 60 + 90 = 150.