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# A parking lot has \$30\$ cars. \$\bullet\$ Each car has either standard transmission or automatic transmission \$\bullet\$ Each car is either bla

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A parking lot has 30 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, Pinto, or Citroen.

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.)

Feb 21, 2020

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There are 1*2*4 = 8 ways of choose the second car so that it is completely different, so the probability is 8/30 = 4/15.

Feb 21, 2020
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Since there are 2*3*5 = 30 possible combinations of the above properties, each possible type of car is represented exactly once. Once we choose the first car, the second car has 2-1=1 possibility for the transmission to be different, 3-1 = 2 possibilities for the color to be different, and  possibilities for the brand to be different. Thus there are 1*2*4 cars that have no properties in common with the first car. We could have chosen this second car in 29 equally-likely ways, and hence our answer is 8/29.

However, thank you for the effort... I really appreciate it... thanks!!

Feb 21, 2020