Let n and m be positive integers with n m 1. (a) (9 points) How many...

 

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Let n and m be positive integers with n m 1. (a) (9 points) How many different m-word sentences can be constructed using an al- phabet of n letters where each of the letters appears exactly once? A sentence is a sequence of words separated by spaces with a period at the end (and there are no other punctuation marks apart from the period character). You may assume that words are comprised of at least one letter and they can be nonsensical. (b) (11 points) How many different m-word paragraphs can be constructed using an alphabet of n letters where each of the letters appears exactly once? paragraph is a sequence of sentences, each containing at least one word. You may also assume that each sentence is comprised of at least one word and is a sequence of words separated by spaces with a period at the end (and there are no other punctuation marks apart from the period character). Finally, words are comprised of at least one letter and they can be nonsensical. Let n and m be positive integers with n m 1. (a) (9 points) How many different m-word sentences can be constructed using an al- phabet of n letters where each of the letters appears exactly once? A sentence is a sequence of words separated by spaces with a period at the end (and there are no other punctuation marks apart from the period character). You may assume that words are comprised of at least one letter and they can be nonsensical. (b) (11 points) How many different m-word paragraphs can be constructed using an alphabet of n letters where each of the letters appears exactly once? paragraph is a sequence of sentences, each containing at least one word. You may also assume that each sentence is comprised of at least one word and is a sequence of words separated by spaces with a period at the end (and there are no other punctuation marks apart from the period character). Finally, words are comprised of at least one letter and they can be nonsensical.