Test: Combinations - GMAT MCQ

Restrictions:
1. He always drives the convertible on Friday
2. Won’t drive the same color vehicle on consecutive days -> He will not drive the blue SUV on Thursday, as on Friday he always drives the Blue Convertible.

Based on the above restrictions, below are the options what he can drive on each day.

This is a perfect scenario to use the total arrangements minus bad arrangements approach.

First, find the total, given that the blue convertible is on Friday: 4 * 3 * 2 * 1 * 1 = 24.

 Next, let’s find the number of arrangements where the blue convertible is on Friday and the blue SUV is on Thursday, violating the second restriction: 3 * 2 * 1 * 1 * 1 = 6. Good = Total - Bad = 24 - 6 = 18.

Alternatively you can look at the number of allowable options on each day, in which case it's helpful to flip the week and think Friday through Monday since your main constraints are on Friday (has to be the convertible) and on Thursday (can't be the blue SUV since he's already driving the blue convertible the next day). This means that you have:

1 option Friday, 3 options Thursday (anything but the two blue cars), 3 options Wednesday (he's already slotted in the convertible and one other car for Friday/Thursday, but now the blue SUV is back in the pool), 2 options Tuesday (anything but the three cars already slotted), and 1 option Monday (whatever's left).
So that calculation is 1 * 3 * 3 * 2 * 1 = 18.