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## Colored Marbles

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #43948 Fun: (2.3) Difficulty: (2.85) Category: Probability Submitted By: javaguru

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?

### Hint

It's simpler to work the problem from both ends.
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