The Ballot Theorem is a result in combinatorial mathematics that deals with counting certain types of paths. Specifically, it provides a way to determine the number of valid sequences of votes in an election where one candidate is always ahead of another. This is particularly useful in scenarios where two candidates receive votes, and we want to ensure that one candidate maintains a lead throughout the counting process. The theorem states that if candidate A receives a votes and candidate B receives b votes, with a > b, the number of ways to arrange these votes such that A is always ahead of B is given by the formula \fraca-ba+b \binoma+ba. This result has applications in various fields, including probability theory and computer science.