Chapter 6.4, Problem 37E

In this exercise we will count the number of paths in thexyplane between the origin (o, o) and point (m, n), wheremandnare nonnegative integers, such

that each path is made up of a series of steps, where each step is a move one unit to the right or a move one unit upward. (No moves to the left or downward are allowed.) Tw^to such paths from (o, o) to (5,3) are illustrated here.

1. Show that each path of the type described can be represented by a bit string consisting of m os and n is, where a 0 represents a move one unit to the right and a 1 represents a move one unit upward.

Conclude from part (a) that there are (*‘* 1 paths of the desired type.