$1.$ A primitive language is based on an alphabet of $10$ unique symbols. All of the words in this language are $6$ symbols long. All of the sentences in this language are $2$ words long.

a$.$ If the words can be constructed from symbols without any restrictions, how many sentences are possible?

b$.$ If every letter in a word must be different from every other letter in that word, how many sentences are possible?

c$.$ If there are $7$ "consonants" and $3$ "vowels" in the alphabet, and each word must contain $4$ consonants and $2$ vowels, and duplicate symbols are allowed in a word, how many sentences are possible?