- #1
Miike012
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How many 8 letter words have 3 vowels constants do not repeat.
Is it
5^3*26*25*24*23*22 ?
Is it
5^3*26*25*24*23*22 ?
Discover the Number of 8 Letter Words with 3 Vowels and Non-Repeating Consonants
- Thread starter Miike012
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SUMMARY
This discussion focuses on calculating the number of 8-letter words containing 3 vowels and non-repeating consonants. The formula proposed includes the use of permutations and combinations, specifically 5^3 for vowels and 26P5 for consonants, while also considering the integration of vowels with consonants. Participants emphasize the importance of order in the arrangement of letters and clarify that the vowels are part of the total 26 letters, which includes 21 consonants. The conversation highlights the need to accurately account for both the selection and arrangement of letters in the final calculation.
PREREQUISITES- Understanding of permutations and combinations
- Familiarity with basic probability concepts
- Knowledge of the English alphabet and its vowel/consonant structure
- Experience with mathematical notation and formulas
- Study the principles of permutations and combinations in detail
- Learn how to apply the formula for combinations, specifically (n choose k)
- Explore examples of word formation problems in combinatorics
- Investigate the integration of different sets in combinatorial calculations
Mathematicians, educators, students in combinatorics, and anyone interested in word formation and probability calculations.
- #2
jedishrfu
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Miike012 said:
Don't you have to also factor in order too:
act vs cat vs some nonsense words like tca, cta ...
cafe vs face
- #3
Miike012
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Another question how do I know when to use the combination equation or permutation equation?
For instance given the example which is posted above are the following strings the same?
A E I M N P Q R
and
E A I M N P Q R
They both contain the same three vowels and the only thing I changed was the placement of the first and second terms
For instance given the example which is posted above are the following strings the same?
A E I M N P Q R
and
E A I M N P Q R
They both contain the same three vowels and the only thing I changed was the placement of the first and second terms
- #4
Miike012
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jedishrfu said:
so I should add 8! ?
- #5
Miike012
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jedishrfu said:
I'm not sure that would work, for instance
A1 B A2
and
A2 B A1
are the same.
I almost feel like I should add (8 choose 3) instead of 8!
- #6
jedishrfu
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Miike012 said:
I think your consonants are unique but your vowels might repeat so you'd also have to factor that in too.
- #7
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Miike012 said:
You mean multiply by 8!?
No, your original formula already has some ordering in it.
For the vowels you have 53, so you've already counted all vowel orders.
Similarly, for the consonants, you used 26P5, not 26C5, so you have those ordered.
All that you are missing is integrating the vowels with the consonants. How many ways are there of doing that?
- #8
vela
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Remember that the vowels are part of the 26 letters. There are only 21 consonants.
- #9
jedishrfu
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vela said:
I missed that, thanks.
- #10
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vela said:
How true
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