If n runners are running in a race and ties are allowed, then how many possible outcomes of the race are there?

Guest Aug 17, 2023

#2**0 **

There are \(n^n\) possible outcomes. Since there are n runners, and there are n amount of finishing positions, the total number of possible outcomes are \(n^n\). This should work if you consider some of the tied positions to be different (eg: tied for second place with two runners and tied for first place with two runners).

takuya0107 Aug 17, 2023