Prize Wheel Odds - 3 slats win a car

I have a 48 slat prize wheel. The wheel has three evenly placed slats. One slat is the front end of the car, the next if the cab, and the last is the back of the car. To win the car you have to get them in order (front to back), in three consecutive spins (48x x48 x 48 which is 110,592 to 1 odds).

My question is what are the odds of hitting all three slats in ANY order, such as back, front, cab?

The first spin has 3 "wins" out of 48, the second has 2 (either of the remaining two slats) out of 48, and the third has 1 out of 48, so the probability of winning is (3 x 2 x 1) / (48 x 48 x 48) = 1 / 18,432.

This includes sets of three spins where you might land on one of the slats more than once (e.g. front, cab, front, which I am not counting as a win).