Question

43 antique cars are in a show, with 1st, 2nd, and 3rd prizes to be awarded. In how many ways can the awards be given?

Answer 1

`74,046`

Explanation:

This is a Permutation question - the order of selection matters (having Car 1, 2, 3 as 1st, 2nd, and 3rd is different than Car 3, 2, 1 as the same 1st, 2nd, and 3rd places).

We have 43 cars and 3 spots, so:

`P_(43,3)=(43!)/((43-3)!)=(43!)/(40!)=(43xx42xx41xx40!)/(40!)`

And so we have:

`43xx42xx41=74,046`