In this tutorial, statistics on the number of people who tie for first place are considered. It is demonstrated that the so-called Rice's method from the calculus of finite differences is a very convenient tool both to rederive known results as well as to gain new ones with ease.
"The number of winners in a discrete geometrically distributed sample." Ann. Appl. Probab. 6 (2) 687 - 694, May 1996. https://doi.org/10.1214/aoap/1034968150