There are 43 people in a room, 23 of which have type A blood, 9 of which have type B blood, 5 of which have type AB blood, and the rest having type O blood. If you are to select a simple random sample of size 15 from this room of individuals, what is the probability that you get eight Type A's, three Type AB's, and the rest equally distributed amongst Type B's and Type O's? Round to 4 decimal places.

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