## Task B-4.4.

On the game board shown in the picture, Ivan needs to get from field $A$ to field $B$. He can only move to a field that is directly to the right or directly above the current field. In how many ways can Ivan get from field $A$ to field $B$?

![](https://cdn.mathpix.com/cropped/2024_05_30_1ebddb66d71be8305afcg-20.jpg?height=323&width=456&top_left_y=444&top_left_x=800)
## First Solution.

If we start from field $A$, we can only reach the field directly to the right in one way, and the same applies to all other fields in that row and the column above field $A$. The number of ways to reach any of the other fields is equal to the sum of the number of ways to reach the field directly to the left and the field directly below. If one of these fields does not exist, the number of ways is equal to the number of ways to reach the previous field (which exists). The table shows the number of ways (obtained by the described addition) to reach each field on the game board.

Thus, we conclude that the total number of ways to get from field $A$ to field $B$ is 500.
![](https://cdn.mathpix.com/cropped/2024_05_30_1ebddb66d71be8305afcg-20.jpg?height=460&width=1474&top_left_y=1318&top_left_x=288)