I love combinatorics problems!
I like to think of these problems as "slots" you have to fill with "marbles" you can pull out of a bag.
In this case, you have three "slots": first place, second place, and third place.
Since there are eight horses competing, you have eight horses or eight "marbles" to draw out of your bag.
Now, look at your first place slot. If you pull a marble out (select a horse in other words), how many marbles are you choosing from? 8.
Now that that's done, choose your horse that will get second place. How many horses/marbles do you have to pull from? 7. Likewise for third place, you only have 6 horses to choose from.
So once you have your slots filled with number of possible options, all you do is multiply the values together.
That's why it's 8*7*6 = number of possible combinations.
