Cards 5

A thing into which you throw a coin and you can then look through it like through a telescope, contains an entire set of 81 Set cards. How many valid sets exist that contain at least one blue card? Sets is a card game. Each Set card has 4 properties: colour, shape, number, and fill. Each of these properties can take on three states on the card. For example, the card can have blue, red, or green colour. The deck contains all different combinations of these properties, each one exactly once (thus a total of 81 cards). A set in the game is called such a triplet of cards that for each of the properties all states on the cards are either the same, or different.

Final Answer:

n =  4782969

Step-by-step explanation:

$$\begin{gathered} C_1(3)=\left(\genfrac{}{}{0ex}{}{3}{1}\right)=\frac{3!}{1!(3-1)!}=\frac{3}{1}=3 \\ n=3^3\cdot 3^4\cdot 3^4\cdot 3^4/\left(\genfrac{}{}{0ex}{}{3}{1}\right)=3^3\cdot 3^4\cdot 3^4\cdot 3^4/3=4782969 \end{gathered}$$

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