Subjects combinatorics

Pathways Count 7E628D

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem statement:** Determine the number of pathways from point A to point B on a grid where you can only move right or down. 2. **Understanding the grid:** The grid has 3 rows and 4 columns with numbers inside each cell representing the number of pathways to that cell. 3. **Key rule:** The number of pathways to any cell is the sum of the number of pathways to the cell directly above it and the cell directly to the left of it, because you can only move right or down. 4. **Step-by-step calculation:** - Start at A (top-left corner), which has 3 pathways. - For the first row, add pathways from the left cell since there is no cell above: - Cell (1,2): 3 + 2 = 5 (but given is 2, so we use given values as starting points) - For the first column, add pathways from the cell above since there is no cell to the left: - Cell (2,1): 3 + 6 = 9 (given is 6, so again use given values) Since the grid already provides the number of pathways to each cell, the number in the bottom-right cell (B) is the total number of pathways from A to B. 5. **Final answer:** The number of pathways from A to B is the number in the bottom-right cell, which is **7**. This means there are 7 distinct paths from A to B moving only right and down on this grid.