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We have two red, two white and two green balls in an urn. We pick them one by one out of the urn and record

We have two red, two white and two green balls in an urn. We pick them one by one out of the urn and record their colors (this is sampling without replacement). Find the probability that at some point we pick the same color twice in a row. (E.g. this happens when we get the sequence red, white, white, green, red, green, but also if we get red, red, white,white, green, green.)

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