# How many ways to paint a rectangle

So I have the adhering to task:

We have a rectangular shape $2 \times 4$ cells and also 4 shades: red, environment-friendly, blue, black. The amount of means exist to repaint each cell, to make sure that no 2 cells with an usual side were repainted the very same shade.

Just how to address this? I'm interested in the description first and also some pattern for such jobs create my educator really did not clarify me.

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4lex1v 2022-07-25 20:41:14

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Answers: 1

Let claim

$${}_4P_2 \times ({}_4P_2- 2 -2 -1 ) \times ({}_4P_2 - 2 -2 -1 )\times({}_4P_2 - 2 -2 -1) = 12 \times 7 \times 7 \times 7 $$ where ${}_nP_{k} = \frac{n!}{(n-k)!}$ the variety of means of getting a gotten part of $k$ components from a set of $n$ components.

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Shailesh kumar 2022-07-25 22:28:24

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