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6 pupils have, between them, won three gold medals, two silver medals and a bronze medal in a painting competition. Unfortunately, their teacher has lost all record of which medals should go to which pupils, so he allocates them by drawing names out of a hat. The first 3 names drawn receive the gold medals, the next two drawn have the silver medals, and the bronze medal goes to the remaining pupil.
How many different ways can the medals be allocated by this method?

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This problem is taken from the UKMT Mathematical Challenges.