Question

31 cars are in a race. In how many different ways can cars finish in order in the top 3 positions?

Answer 1

In this case the order in the top 3 positions matters, also we can repeat a car in two different positions, therefore, we must use permutations.

Now, in the top 3

There are 31 different ways to be in the first place, then the are 30 ways that the cars can be in the second place, finally, there are 29 ways to be in third place. All this assumes that when a car is in any place it can not be repeated.

Then :

31 * 30 * 29 = 26970 different ways.