Chapter 16, Problem 8CT

To determine

To find: The number of routes that take from point $A$ to $B$ .

Answer to Problem 8CT

The number of represented routes from point $A$ To $B$ are $\begin{array}{c}A\\ B\\ C\\ D\end{array}\left[\begin{array}{l}\begin{array}{cccc}A& B& C& D\end{array}\\ \left[\begin{array}{cccc}0& 1& 1& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 1& 1& 1& 1\end{array}\right]\end{array}\right]$ .

Explanation of Solution

Given information:

The given figure is

  

Calculation:

Consider the representation of matrix is.

  $\begin{array}{c}A\\ B\\ C\\ D\end{array}\left[\begin{array}{l}\begin{array}{cccc}A& B& C& D\end{array}\\ \left[\begin{array}{cccc}0& 1& 1& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 1& 1& 1& 1\end{array}\right]\end{array}\right]$

Therefore, the number of represented routes from point $A$ to $B$ are $\begin{array}{c}A\\ B\\ C\\ D\end{array}\left[\begin{array}{l}\begin{array}{cccc}A& B& C& D\end{array}\\ \left[\begin{array}{cccc}0& 1& 1& 1\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 1& 1& 1& 1\end{array}\right]\end{array}\right]$ .