Calculating Routes on a Grid: Using Combinations and Pascal's Triangle

In summary, the conversation is about finding the number of routes from point A to point B in a city laid out in a rectangular grid, only traveling north or east. The question asks how many of these routes pass through a specific intersection, and the person has solved similar questions before but is unsure of the answer. Another person points out an error in their calculation.
  • #1
SeththeBaller
13
0
1. The streets of a city are laid out in a rectangular gird, as shown below

pbmlY.png


a) Use combinations to find the number of routes through the grid that lead from point A to point B by only traveling north or east. Show your calculations

b) How many of these routes pass through intersections C



2. Alright, so I've solved similar questions before. I get to P(66,6)/6! only to get some absurd answer. I understand that from point A to point B there is a distance of 66 blocks-11 east, 6 north. Somehow I believe that the exponential answer that comes from this is not what my professor expects.

I was wondering if I could have help with this please and thank you :D
 
Last edited:
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  • #2
How did you get 66 blocks? No matter how you travel, the most you could possibly get is 17 (11 east + 6 north). Multiplying gives you the area, not the distance.
 
  • #3
Whoops, lmao, sorry long day, that makes so much sense, I know what to do from here lol
 
  • #4
Np, I know the feeling, gl :P
 

Related to Calculating Routes on a Grid: Using Combinations and Pascal's Triangle

1. What is a grid?

A grid is a pattern of intersecting horizontal and vertical lines that form squares or rectangles. It is commonly used to organize and display data or to solve mathematical problems.

2. What is Pascal's Triangle?

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it. It is named after the mathematician Blaise Pascal and has many applications in mathematics, including in probability, combinatorics, and algebra.

3. How is Pascal's Triangle related to grids?

Pascal's Triangle can be represented as a grid where the numbers are arranged in a triangular pattern. Each row of the triangle represents the coefficients of the binomial expansion (a+b)^n, where n is the row number.

4. What are some uses of grids and Pascal's Triangle in science?

Grids and Pascal's Triangle are commonly used in science to solve problems involving patterns, combinations, and probabilities. They can also be used to model biological growth patterns and to analyze data in various fields such as physics and genetics.

5. How can one create a grid and Pascal's Triangle?

A grid can be created by drawing intersecting lines on a sheet of paper or using software programs such as Microsoft Excel. Pascal's Triangle can be created using a simple algorithm or by using the choose function in a programming language such as Python. There are also several online tools and apps available for generating Pascal's Triangle.

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