(Solved): 4. Determine the number of 9-letter words with no repeated letters in the alphabet \( \{a, b, c, d ...

4. Determine the number of 9-letter words with no repeated letters in the alphabet \( \{a, b, c, d, e, f, g, h, i\} \) (a) in which the letters \( a, b, c \) appear consecutively in some order. (b) in which either \( a b \) or \( c d \) (or both) appear as consecutive subwords. \( { }^{3} \) (c) in which neither \( a b \) nor \( c d \) appear as consecutive subwords. (d) Find the number of 9-letter words that have a repeated letter. Hint: Use the difference theorem. \( { }^{3} \mathrm{~A} \) consecutive subword of a word is a sequence of letters that appear consecutively in the original word.