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Hogwarts has 4 houses (Gryffindor, Hufflepuff, Ravenclaw, Slytherin). We can represent them by their first letters...

Hogwarts has 4 houses (Gryffindor, Hufflepuff, Ravenclaw, Slytherin). We can represent them by their first letters G H R S. Each house has exactly 20 students. If I choose 5 students randomly, what is the probability that I have more Gs than all the other houses put together?

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