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2022 MMATHS Team Online p6 - word by 5 different letters

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October 1, 2023
combinatoricsMMATHS

Problem Statement

Prair writes the letters A,B,C,DA,B,C,D, and EE such that neither vowel are written first, and they are not adjacent; such that there exists at least one pair of adjacent consonants; and such that exactly five pairs of letters are in alphabetical order. How many possible ways could Prair have ordered the letters?
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