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The Krilandic language over the alphabet $\Sigma = \{ \mathsf{A,B,C,D,E} \} $ consists of all $6$-letter words without a letter repeating twice successively. In what place does the word $\mathsf{DEBABE}$ appear in a Krilandic dictionary (listing all Krilandic words, lexicographicly)?

I know how to calculate the number of such words using the inclusion–exclusion principle, but how is this helpful here?

Tony Erwin
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  • You should just count the words that come before DEBABE. How many start with A? – Ross Millikan Jan 11 '23 at 06:16
  • Your question looks like https://math.stackexchange.com/questions/4616018/the-letters-b-e-i-m-o-z-are-arranged-in-alphabetical-order-in-a-list-where/4616028#4616028 just with a few more restrictions. –  Jan 11 '23 at 06:23
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    I think this question is not enough like the one cited by @youthdoo to be considered a duplicate. It seems more difficult in the allowing of multiple appearances of the same letter as long as they aren't adjacent. – coffeemath Jan 11 '23 at 06:38
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    You can try a "brute force" approach: 1) how many strings wit A first? (maybe $4 \times 4 \times 4 \times 4$?) Then 2) how many with B? and how many with C? Then 3) count the DA and DB and DC. Then 4) count the DEA, and so on. – Mauro ALLEGRANZA Jan 11 '23 at 07:34
  • Yes, so we shall be in search of a better solution. –  Jan 11 '23 at 07:34
  • I'm not quite sure what twice successively means. I suppose that AABCDE is allowed and AAAABC is not, but what about AAABCD? – Peter Phipps Jan 11 '23 at 14:47

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