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The people living on the island of Gibberish use the standard Kobish alphabet ( letters, A through T). Each word in their language is 4 letters or less, and for some reason, they insist that all words contain the letter A at least once. How many words are possible?

 May 28, 2018
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The people living on the island of Gibberish use the standard Kobish alphabet ( letters, A through T).

Each word in their language is 4 letters or less, and for some reason,

they insist that all words contain the letter A at least once.

How many words are possible?


\(\begin{array}{|lr|} \hline \text{words with $1$ letter : } &1 \\ \text{words with $2$ letters: } &39 \\ \text{words with $3$ letters: } &1141 \\ \text{words with $4$ letters: } &29679\\ \hline \text{sum: } & 30860 \\ \hline \end{array} \)

 

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 May 28, 2018

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