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A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in this stock. There are 5 places in a row in his show case. The number of different ways of displaying the three varieties of perfumes in the show case is _______.

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Detailed Solution

Let Three types be A, B, C
$\begin{matrix} A \\ B \\ C \end{matrix} \begin{matrix} A \\ B \\ C \end{matrix} \begin{matrix} A \\ B \\ C \end{matrix} \begin{matrix} B \\ C \\ A \end{matrix} \begin{matrix} C \\ A \\ B \end{matrix}} 3 \frac{5!}{3!}$
$\begin{matrix} A \\ A \\ B \end{matrix} \begin{matrix} A \\ A \\ B \end{matrix} \begin{matrix} B \\ C \\ C \end{matrix} \begin{matrix} B \\ C \\ C \end{matrix} \begin{matrix} C \\ B \\ A \end{matrix}} 3 \frac{5!}{2! 2!}$

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