OK, I got the answer but not on my own, LOL!
The answer is 24 and the calculation is 4 x 3 x 2 x 1. How they KNEW that, I have no idea.
If the runners were assigned letters ABCD, it would come out like this:
ABCD, ABDC, ACDB, ACBD, ADBC, ADCB
BACD, BADC, BCAB, BCDA, BDAC, BDCA,
CABD, CADB, CBDA, CBAD, CDAB, CDBA
DABC, DACB, DBAC, DBCA, DCAB, DCBA
WHEW!!! Now, except for kids' homework, when am I going to need to KNOW this?!