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Answer:
504 arrangements are possible
Step-by-step explanation:
Arrangements of n elements:
The number of arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
Arrangements of n elements, divided into groups:
The number of arrangements of n elements, divided into groups of [tex]n_1, n_2,...,n_n[/tex] elements is given by:
[tex]A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]
In this case:
9 pens, into groups of 5, 3 and 1. So
[tex]A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504[/tex]
504 arrangements are possible