Question

Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian requires \(c\) consonants and \(v\) vowels, where \(c > 0\), \(v > 0\), and \(c > v\). Express the number of possible Martian nouns in terms of \(c\) and \(v\). Your answer need not be in closed form.

1. \(c + v\)
2. \(c^2 - v^2\)
3. \(c \times v\)
4. \(2^{c+v}\)

Answer 1

The number of possible Martian nouns is dependent on the structure of the language and can be modeled by the product of consonants and vowels, c \times v, if every noun is assumed to be made of one consonant and one vowel.

Step-by-step explanation:

The number of possible Martian nouns, assuming Martian language rules are similar to combinatorial rules of Earth languages, would depend on the allowed structures for nouns. If Martian nouns require at least one consonant and one vowel and any combination is allowed without repetition, the number could be simply c \times v.

However, without specific rules on the structure of Martian nouns, determining the exact number of possibilities is difficult. Knowing the minimum and maximum length of the nouns, as well as whether letters can be repeated, would also affect the count.

Assuming a simplistic model where each noun is made of one vowel and one consonant, the number of possible Martian nouns would be the product of the number of consonants and vowels, or c \times v.