1. Consider a grid with (0, 0) at the bottom left corner and (m, n) at the top right corner. Suppose you start at the bottom left corner of the grid and want to make your way to the top right corner as fast as possible by moving only up or right. How many different fastest routes are possible. Explain.

2.

Please answer both or none. Thanks a lot.

Use the binomial theorem to prove that ? 2 C(n ,J) = 3n 0