Starting in the top left corner of a $2\times2$ grid made out of single $1\times1$ squares, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there in a $20\times20$ grid?

You may use a calculator for the final step of your calculation.

**
Hint
**
:
Pascal's triangle
.

The answer is 137846528820.

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This is a direct application of the rectangular grid walk . There is a total of $\dbinom{20+20}{20} = \dbinom{40}{20} =\boxed{137846528820}$ paths from the top-left corner to the bottom-right corner.