The question is :Given two candidates that got n votes each , what is the number of ways to count the 2n votes while one candidate is leading all the time.
I tried to solve it using Catalan numbers but I'm not sure about the way i'm thinking I thought that the it's equal to start in the grid from (1,0) to (n+1,n) in this way both the candidates are having n votes at the end and the number of ways to do this without touching the diagonal are equal to $\frac{1}{n+1}\ * \binom{2n}{n} $ .