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# help

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Jay owns a fleet of 24 shiny cars.

Each car has either standard transmission or automatic transmission
Each car is either black, white, or red
Each car is either a Toyota, Mercedes-Benz, Chevrolet, or Pinto

No two cars are the same for each of the three categories. (For example, no two cars have standard transmission, are white, and Toyotas.)

Two of the cars are chosen at random. What is the probability that the two cars differ in all three categories? (For example, a black Chevrolet with standard transmission is different in all three categories from a red Pinto with automatic transmission, but not from a black Mercedes-Benz with automatic transmission.)

Nov 29, 2019

#1
+24407
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Two of the cars are chosen at random.

What is the probability that the two cars differ in all three categories?

I assume,

$$\begin{array}{|rcll|} \hline && { 24\times 1 \times 2 \times 3}\above 1pt \dfrac{24!}{(24-2)!} \\\\ &=& \dfrac{144}{552} \\\\ &=& 0.26086956522\ \approx 26\% \\ \hline \end{array}$$

Nov 29, 2019