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By the sum rule we can count the number of strings of length 4 or less by counting the number of strings of length i, for 0 <= i <= 4, and then adding the results. Now there are 26 letters to choose from, and a string of length i is specified by choosing its characters, one after another. Therefore, by the product rule there are 26^i strings of length i.

The answer to the question is thus:

sum i=0 to 4 ( 26^i = 1 + 26 + 676 + 17576 + 456976) = 475,255.

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Q: How many strings are there of lower case letters of length 4 or less?
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