Find the number of 6-letter words that use letters from {A, B, C, D, E} in which no 5 consecutive letters are all the same. (Hint. First count the words that you don't want to include.)
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First, we count the total number of 6-letter words that can be formed using the given 5 letters. Since each position can be filled with any of the 5 letters, there are $5^6$ possible words. Show more…
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