Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A? The solution is a Catalan number C_n. A related problem also called "the" ballot problem is to let A receive a votes and B b votes with a>=b. This version of the ballot problem then asks for the probability that A stays ahead of B as the votes are counted. The solution is (a - b + 1)/(a + 1), as first shown by M. Bertrand. Another elegant solution was provided by André using the so-called André's reflection method. The problem can also be generalized. Furthermore, the TAK function is connected with the ballot problem.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.
Club Z! has connected me with a tutor through their online platform! This was exactly the one-on-one attention I needed for my math exam. I was very pleased with the sessions and ClubZ’s online tutoring interface.
My son was suffering from low confidence in his educational abilities. I was in need of help and quick. Club Z! assigned Charlotte (our tutor) and we love her! My son’s grades went from D’s to A’s and B’s.
I’ve been using Club Z’s online classrooms to receive some help and tutoring for 2 of my college classes. I must say that I am very impressed by the functionality and ease of use of their online App. Working online with my tutor has been a piece of cake. Thanks Z.
Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+.
Sarah is very positive, enthusiastic and encourages my daughter to do better each time she comes. My daughter’s grade has improved, we are very grateful for Sarah and that she is tutoring our daughter. Way to go ClubZ!
