# Clever counting » Routes in a grid

*Example*

How many routes are there from `A` to `C` via `B`, without detours?

Answer:

A route from `A` to `B` without detours consist of 6 steps.

For example `ENENEE`. 2 steps `N`orth and 4 steps `E`ast.

This has to apply to every route from `A` to `B`, so how many routes are possible that consist of 2`N` and 4`E`?

You can calculate that is:

6

2 = 6 · 52 · 1 = 6 nCr 2 = 15

In the same way you can calculate the number of routes from `B` to `C`:

7

3 = 7 · 6 · 53 · 2 · 1 = 7 nCr 3 = 35

So the total number of routes is: 15 × 35 = 525