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We have 9 pens, of which 5 are green ink, 3 are red ink, and 1 is black. If we put the pens in a line, how many arrangements are possible

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Answer:

504 arrangements are possible

Explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by:


A_(n) = n!

Arrangements of n elements, divided into groups:

The number of arrangements of n elements, divided into groups of
n_1, n_2,...,n_n elements is given by:


A_(n)^(n_1,n_2,...,n_n) = (n!)/(n_1!n_2!...n_n!)

In this case:

9 pens, into groups of 5, 3 and 1. So


A_(9)^(5,3,1) = (9!)/(5!3!1!) = 504

504 arrangements are possible

User Yassine Sedrani
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