I cannot make an intuitive sense of a shortcut to calculate the sample space but my answer was 720.

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My way of approaching this would be to note that a car needs one (and only one) of "Model", "Luxury Level" and "Colour". This means that you effectively have 3 "gaps"/categories that need to be filled.

In the first gap, we need a model; second gap, a Luxury Level; and third gap, a colour. Also, I think it's fairly safe to assume that \(M_1L_2C_3\) is the same as \(L_2C_3M_1\) so there's no complication there.

Now, there are 4 different models and each of those models can have 3 different luxuries. Each of those model/luxury combinations can then have 1 of 6 different colours i.e. for each model, we can have 3 luxury levels, and for each of those we can have 6 different colours (it might help to picture it as a tree diagram - but don't actually draw it since there are lots of combinations!).

This leads to the number of elemnets in the sample space being \(4\times 3 \times 6=72\)

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