Question

There are 24 cars in the parking lot outside of my building. They are all either 2-door or 4-door, are either white, black, or red, and are either Ford, Toyota, BMW, or Volkswagen. No two cars are the same with respect to these properties (in other words, for example, there are no two 4-door red Toyotas). If 2 cars are chosen at random, then what is the probability that they are different in all three of these properties? (For example, a 2-door white BMW is different from a 4-door black Ford, but not from a 4-door white Volkswagen).