A bucket contains 11 letters....

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SUMMARY

The discussion centers on calculating the number of 7-letter words that can be formed using 3 vowels and 4 consonants from a set of 11 letters, consisting of 5 vowels and 6 consonants. The initial calculation proposed was 5C3 x 6C4 x 7!, which was deemed incorrect by peers. The conversation highlights the ambiguity in the problem statement regarding the rules of word construction, such as whether specific arrangements or a dictionary search are necessary for valid words.

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  • Understanding of combinatorial mathematics, specifically combinations (nCr).
  • Familiarity with factorial notation and its application in permutations.
  • Basic knowledge of vowel and consonant classification in the English language.
  • Awareness of word construction rules in linguistics.
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  • Research combinatorial methods in word formation.
  • Learn about the application of factorials in permutations and combinations.
  • Explore linguistic rules governing valid word structures.
  • Investigate dictionary-based approaches for validating word combinations.
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This discussion is beneficial for mathematicians, linguists, educators, and students engaged in combinatorial problems and word formation challenges.

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A bucket contains 11 letters: 5 vowels and 6 consonants.
How many 7 letter words can you make if you use 3 vowels and 4 consonants?

I think the ans should be 5C3x6C4x7!
but they say this is wrong at college.

Any help is appreciated. Thank you
Mentor note: Changed thread title to agree with problem statement.
 
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What is the answer supposed to be? If you've stated the problem correctly then I agree with your answer.
 
Are there any rules about word construction? Can it be any 3 vowels and any 4 consonants in any order? Does it have to be CVCVCVC? Etc.
 
mjc123 said:
Are there any rules about word construction? Can it be any 3 vowels and any 4 consonants in any order? Does it have to be CVCVCVC? Etc.
But that would require a dictionary search, specification of the language, etc. I can't believe that the question was meant to require such things.
 
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