There are 5^10 possible words of length 10 in the alphabet {a, b, c, d, e}. Of these, 3^10 do not contain a and b next to each other. This is because, for each position in the word, there are three choices (c, d, or e) that do not violate the constraint.
5^9 are words that do not contain a and b next to each other. This is because there are 5^9 ways to choose the positions of the a's and b's, and for each of these choices, there are 5 ways to choose the letter at each position.Therefore, the probability that a randomly chosen word of length 10 does not contain a and b next to each other is 3^10/5^10.
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