I Have a Problem!

Hi, I have a problem which I do not know the answer to. Two ants start on the origin of a coordinate grid, and keep going right and up until they reach (5,5), and can not go farther than (5,5). Every time they get to a new point, the 1st ant puts a blue dot, and the second one puts a red dot. What is the probability that there will be 5 purple dots? The Ants DO put a purple dot at the origin and at (5,5).

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$