determine the number of different possible routes that tyler can travel from point a to point b if he…

Explanation:

Step1: Identify total moves

Let's assume moving north is one - type of move and moving west is another. Suppose moving from A to B requires $m$ moves north and $n$ moves west. If we assume the grid has a horizontal length of $x$ units and a vertical length of $y$ units from A to B, here assume the horizontal distance from A to B is 5 units and the vertical distance is 5 units. So the total number of moves from A to B is $m + n=5 + 5=10$ moves in total.

Step2: Use combination formula

The number of ways to arrange these moves is given by the combination formula $C(m + n,n)=\binom{m + n}{n}=\frac{(m + n)!}{n!m!}$. Here $m=n = 5$, so we calculate $\binom{10}{5}=\frac{10!}{5!×(10 - 5)!}=\frac{10!}{5!×5!}$. [ \begin{align*} \frac{10!}{5!×5!}&=\frac{10\times9\times8\times7\times6\times5!}{5!\times5\times4\times3\times2\times1}\ &=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}\ &=252 \end{align*} ]

Answer:

252