Question

Using the nouns N = {cat, rat, snake, fish} and the verbs V = {bites, eats, kicks}, how many "sentences" of the form

noun

verb

noun

are there, with the restriction that every word in the sentence has a different length? (For example, "cat eats snake" is such a sentence, but "rat bites cat" is not, because it contains two words of length three.) Use a decision tree to arrive at your answer.