MathProbabilityEvents and probabilities

Calculating cardinality

Color palette dilemma

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The RGB color model encodes any color as a combination of three colors: red, green and blue:

The range of acceptable values for each component is from $0$ to $255$ . How many ways are there to choose $500$ colors using the RGB model?

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C_{256!}^{256!-500}

C_{256 \cdot 3}^{500}

C_{256^3}^{256^3-500}

C_{255^3}^{255^3-500}

C_{256 \cdot 3}^{256 \cdot 3-500}

C_{256^3}^{500}

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