Answer to Question #198916 in Combinatorics | Number Theory for angel

Question

In horse racing, a trifeta is a type of bet. To win a trifeta bet, you need to specify the horses that finish in the top three spots in the exact order in which they finish. If eight horses enter the race, how many different ways can they finish in the top three spots?

Answer 1

For the first place there are 8 different ways. After that for the second place there are 7 different ways, and then for the third place there are 6 different ways. It follows that by the combinatorial product rule the horses finish in the top three spots in $8\cdot 7\cdot 6=336$ different ways.