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# Number Theory/Enumerating call letters

Question
Radio stations in the United States that are east of the Mississippi River have call letters consisting of a W followed by three letters (W can be used again). How many different call letters of this type are possible? My book says 17,576 but does not break it down, nor does it provide a similar practice problem. I figure the alphabet has 44 letters and I got stuck after that. Can you explain the logic (if any) in getting this answer? Thank you.

I'm not sure where the 44 came from, but the alphabet, A to Z, only has 26 letters.

Since 26*26 = 520 + 156, and that is 676, that is the number for two letters.
Since 26*676 = 13,520 + 4,056 = 17,576, that is the number for three letters.

The first few powers of 26 are
26
676
17,576
456,976
11,881,376
308,915,776
8,031,810,176
208,827,064,576
5,429,503,678,976

I find it interesting that one 26 squared, all of the rest of the powers end in 76.

Number Theory

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