Combinatorics: Solve No Vowel Arrangement

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SUMMARY

The problem involves arranging the letters of the word "CONSTANTINOPLE" such that no two vowels are adjacent. The word consists of 14 letters, including 6 vowels (O, A, I, O, E) and 8 consonants (C, N, S, T, N, T, N, P, L). The solution requires calculating the arrangements of consonants first and then inserting vowels in the gaps created by consonants to ensure they are not adjacent. The final count of valid arrangements is determined through combinatorial methods.

PREREQUISITES
  • Understanding of combinatorial principles
  • Familiarity with permutations and arrangements
  • Knowledge of vowel and consonant identification in words
  • Basic grasp of factorial calculations
NEXT STEPS
  • Study combinatorial arrangements with restrictions
  • Learn about permutations of multiset, particularly with repeated elements
  • Explore the concept of gaps in arrangements for non-adjacency
  • Practice similar problems involving vowel-consonant arrangements
USEFUL FOR

Students studying combinatorics, educators teaching permutation concepts, and anyone interested in solving arrangement problems with specific constraints.

Roohul Amin
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please help solving this question
The letters of the word CONSTANTINOPLE are written on 14 cards, one on each card. The cards are shuffled and then arranged in a straight line: how many arrangements are there where no two vowels are next to each other?
 
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