There are three horses: Uri, Uli and Buki. Results that can be possible in the race are 13.
- Uri first, Uli second, Buki third.
- Buki first, Uri second, Uli third.
- Buki first, Uri and Uli second together.
- Uri and Buki first, Uli second.
- Uri, Buki and Uli first all together.
There are eight more possible results but didn't write them all because I guess you understand what I mean. Given that information, they ask to calculate how many different possible results can be with 5 horses.
I can calculate how many results can be if all the horses come at different times:
$120 = 5\cdot4\cdot3\cdot2\cdot1$
How do I do it with the other cases? Please don't use complicated math, famous formulas or theoremas, I'm supposed to calculate this just with logic.