What is the permutation of words a-z created with the pattern: cvcvcv where c = a consonant and v = vowel?

Question

What is the permutation of words a-z created with the pattern: cvcvcv where c = a consonant and v = vowel?

I want to know because I have a software that creates rooms with that name pattern and I want to know how many unique rooms there can be.

Thanks

Answer 1

Assuming that all the vowels are the same, and all the consonants are the same: You have $5$ possible choices for the vowel, and $21$ possible choices for the consonant, and each combination gives a unique word. So, you have $5*21 = 105$ unique room names.

On the other hand, if the vowels and consonants are allowed to be different from each other, you have $5^3$ choices for all the vowels, and $21^3$ choices for all the consonants, for a total of $5^3\times21^3=1157625$ names.

Answer 2

Taking $cvcvcv$ how many times can you order it to form different arrangements? Three consonant and three vowels are being repeated so $\frac{6!}{3!3!} = 20$ different arrangements.

But now since each vowel has $5$ possibilities and each consonant has $21$ possibilities, then $20\cdot 5^3\cdot 21^3$