In a simple language, there are only three letters: A, B and C. Any combination of...

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In a simple language, there are only three letters: A, B and C. Any combination of A's, B's and C's forms a word, with the condition that no word can contain "BC" (that is, there can never be a C immediately after a B). Let f(n) be the number of words of length n. (a) Determine the values of f(1), f(2) and f(3). (b) If n ≥ 2, explain why the number of words of length n that end with a B is equal to f(n-1). (c) Determine, with justification, a recursive formula for f(n). (d) Determine the value of f(10). In a simple language, there are only three letters: A, B and C. Any combination of A's, B's and C's forms a word, with the condition that no word can contain "BC" (that is, there can never be a C immediately after a B). Let f(n) be the number of words of length n. (a) Determine the values of f(1), f(2) and f(3). (b) If n ≥ 2, explain why the number of words of length n that end with a B is equal to f(n-1). (c) Determine, with justification, a recursive formula for f(n). (d) Determine the value of f(10).

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