Finding the Number of Lines from A to B in a 4x7 Rectangle

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SUMMARY

The discussion centers on calculating the number of distinct paths from point A to point B in a 4x7 rectangle, where movement is restricted to upward and rightward steps. The problem can be framed as a combinatorial challenge, specifically using the concept of combinations to determine the number of ways to arrange the steps. The total number of steps required is 11, consisting of 4 upward moves and 7 rightward moves. The solution involves calculating the binomial coefficient, represented as C(11, 4) or C(11, 7), to find the total number of unique paths.

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  • Understanding of combinatorial mathematics
  • Familiarity with binomial coefficients
  • Basic knowledge of pathfinding in grid-based problems
  • Ability to perform factorial calculations
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  • Study combinatorial pathfinding techniques in grid layouts
  • Learn about binomial coefficients and their applications
  • Explore factorial calculations and their role in combinations
  • Investigate similar problems involving restricted movement in grids
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Homework Statement


The number of lines from A to B if you must travel along the lines going up and right is...
(there is a rectangle with that has 4 cubes going down vertically and 7 horizontally (4x7) and a is at the bottom left, be is at the top right)
 
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mocogi said:

Homework Statement


The number of lines from A to B if you must travel along the lines going up and right is...
(there is a rectangle with that has 4 cubes going down vertically and 7 horizontally (4x7) and a is at the bottom left, be is at the top right)

Hello mocogi. Welcome to the Forum. Normally to receive help in this forum you are expected to show what thought or work you have applied to your problem.

I suppose you mean "squares" instead of cubes. I will give you a little hint. Considering each move to the right or up as a "step", how many total steps do you need? How many ways can you choose which steps to use for the up moves?
 

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