In Problem 21, how many different paths are there from A to B that go through the point circled in the following lattice?

# In Problem 21, how many different paths are there from A to B that go through the point circled in the following lattice?

J
Asked by 2 years ago
240 points

In Problem 21, how many different paths are there from A to B that go through the point circled in the following lattice?

In Problem
jeffp

Answered by 6 months ago
100 points

Why is a multiplication instead of an addition I thought 4C2 + 3C2 … Thanks

Answered by 2 years ago
8.7k points

This is a continuation of a question answered here,

https://www.lil-help.com/questions/7812/consider-the-grid

so in this case we have to move through the grid point that is circled.

We can think of this as moving first from point A to the circle (it takes 4 moves to get there -- 2 ups and 2 rights). To get to the circle there are a total of,

$$\frac{4!}{2!2!} = 6$$ different ways to go.

To get from the circle to the point B we need to make a total of 3 moves -- 1 up and 2 right,

$$\frac{3!}{2!1!} = 3$$ different ways to go.

so there are a total of $6 \cdot 3=18$ ways to traverse the path from A to B.

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