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Colored Marbles
Tim, Ted and Tom each have a bag containing five different colored marbles. Each bag contains the same five colors.
Tim reaches into Ted's bag and Tom's bag and randomly withdraws a marble from each and places them in his bag. Ted then reaches into Tim's bag and Tom's bag and randomly removes a marble from each and places them in his bag. Finally, Tom reaches into Tim's bag and Ted's bag and randomly chooses a marble from each and places them in his bag.
What is the probability that each has five different colors of marbles in their bag?
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