# Number of ways to go to the opposite corner.

• ssd
In summary, there are m+1 parallel roads going north-south and n+1 parallel roads going east-west. The question asks for the number of ways to travel from the northeast corner to the southwest corner, heading either west or south. The recommended method is to use words representing directions and use bijection to convert them into paths. This can be reinforced with exercises and thinking about which words correspond to a path from corner to corner.
ssd
# of ways to go to the opposite corner.

Suppose m+1 parallel (laid N-S)roads cross n+1 parallel (laid E-W) roads. In how many different ways one can move from North- East corner (of crossing) to South- West corner heading either West or South? What the simplest / attractive way (explanation) to make students of age 17yr understand while teaching in class. I observed, students really do not get the logic.

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The usual way to do this is to write paths as words in the letters "S" and "W", and count how many of those words correspond to a path from one corner to another, right?

I imagine the best way would be to make them understand the bijection. Exercises converting from words to paths and back. Have them think about which words correspond to a path from corner to corner.

Nice.

## 1. How can I calculate the number of ways to go to the opposite corner?

The number of ways to go to the opposite corner can be calculated using the binomial coefficient formula, where n is the number of moves and r is the number of moves in a certain direction. The formula is (nCr) = n! / (r! * (n-r)!).

## 2. What is the significance of determining the number of ways to go to the opposite corner?

Determining the number of ways to go to the opposite corner can help in understanding the complexity of a problem, and can also be useful in optimization and decision making processes.

## 3. Can the number of ways to go to the opposite corner be calculated for any given starting point?

Yes, the number of ways to go to the opposite corner can be calculated for any given starting point, as long as the dimensions of the grid are known.

## 4. Is the number of ways to go to the opposite corner affected by the shape or size of the grid?

Yes, the number of ways to go to the opposite corner is affected by the shape and size of the grid. It is important to take into consideration the dimensions of the grid when calculating the number of ways.

## 5. Are there any real life applications of the concept of number of ways to go to the opposite corner?

Yes, the concept of number of ways to go to the opposite corner can be applied in various fields such as computer science, mathematics, and game theory. It can also be used in real life scenarios, such as finding the shortest path in a maze or determining the possible outcomes in a game of chess.

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