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HMMT November 2009 U10

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Admiral Ackbar needs to send a 5-character message through hyperspace to the Rebels. Each character is a lowercase letter, and the same letter may appear more than once in a message. When the message is beamed through hyperspace, the characters come out in a random order. Ackbar chooses his message so that the Rebels have at least a 12\frac{1}{2} chance of getting the same message he sent. How many distinct messages could he send?

Dataset text NuminaMath olympiads. Quoted with source.

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26

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