The Hawaiian alphabet consists of $12$ letters, the vowels a, e, i, o, u and the consonants h, k, l, m, n, p, w.
Show that $20,736$ different $4$-letter ‘‘words’’ could be constructed using the $12$-letter Hawaiian alphabet.
My answer: Isn't it $12 \cdot 11 \cdot 10 \cdot 9= 11880$?
On
The other commentator is correct but I feel there can be a better explanation. The fundamental counting principle is as follows: $$\prod_{i=1} ^{n} c_i $$ Where $c_i$ is the number of choices at i. Since in this case we allow any random sequence of characters, $c_i$ will be 12 at all 4 (n) points in the word. Hence the answer, $12^4$ or 20,736.
No, because you don't need 4 different letters in the word. The answer is $(12)^4,$ since each letter has 12 possibilities.