MathDB

There are

5

accents in French, each applicable to only specific letters as follows:
[*] The cédille: ç [*] The accent aigu: é [*] The accent circonflexe: â, ê, î, ô, û [*] The accent grave: à, è, ù [*] The accent tréma: ë, ö, ü
Cédric needs to write down a phrase in French. He knows that there are

3

words in the phrase and that the letters appear in the order:

cesontoiseaux.

He does not remember what the words are and which letters have what accents in the phrase. If

n

is the number of possible phrases that he could write down, then determine the number of distinct primes in the prime factorization of

n

Problem Statement