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Since any two letters of the alphabet do not duplicate each other, then the number of arrangements of any two letters is the same as the number of permutations of 26 things taken 2 at a time. That is 26! / (26 - 2)!, or 26! / 24!, or (26) (25), or 650.

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Q: How many different ways can any two letters of the alphabet be arranged?
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