We can use a grid to represent Josh's movements. The number of ways for Josh to travel from (0,0) to (6,7) can be represented by the number of paths from the top-left corner to the bottom-right corner of a 6 by 7 grid, moving only up or right.
To calculate this, we can use Pascal's Triangle. Each point on the grid represents a number, starting from 1 at the top-left corner, and each number represents the number of ways to reach that point from the top-left corner.
By using Pascal's Triangle, we can fill in the grid accordingly:
\[
\begin{array}{ccccccc}
1 & 1 & 1 & 1 & 1 & 1 & 1 \\
1 & 2 & 3 & 4 & 5 & 6 & 7 \\
1 & \boxed{3} & 6 & 10 & 15 & 21 & 28 \\
1 & 4 & 10 & 20 & 35 & 56 & 84 \\
1 & 5 & 15 & 35 & 70 & 126 & 210 \\
1 & 6 & 21 & 56 & 126 & 252 & 462 \\
1 & 7 & 28 & 84 & 210 & 462 & 924 \\
\end{array}
\]
Therefore, there are $\boxed{28}$ ways for Josh to reach his home.
Josh starts at the point (0,0) and needs to travel to his home at the point (6,7). There is a fire at the point (2,3) so he cannot travel there. How many ways are there for Josh to reach his home if he can only move up or right?
1 answer