Answer to Question #117088 in Combinatorics | Number Theory for Priya

Question

How many words of 10 letters can you form using the Italian alphabet? (there are 21 different letters in the Italian alphabet or which 5 are vowels.)

Answer 1

We have no conditions concerning the structure of word, so we may define the word as the arbitrary consequence of 10 letters. We can also use each letter any number of times, therefore we have 21 variants to choose the first letter of our word, we also have 21 variants to choose the second letter of our word, and so on. So the total amount of words will be

$21\cdot21\cdot \ldots = 21^{10}= 16679880978201.$