12 Oreo cookies

Probability Level 4

Alexane has 12 oreo cookies of which 9 are the regular type and 3 are golden type.
She wants to share her oreos with her 3 friends Jose, Amy, and Camille.
She puts the 12 oreos in a brown bag and she and her 3 friends each randomly choose 3 oreos.

What is the probability that exactly one of them ends up with all 3 golden oreos?

If the probability can be expressed as ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.


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