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If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are
ways of picking the vowels, and
ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is
Keep in mind that this means words like TRIES and TIRES are treated as different.