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The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is?
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The number of six letter words (with or without meaning), formed using...
Understanding the Problem
To find the number of six-letter words formed from the letters of the word "VOWELS" such that all consonants do not come together, we start by identifying the letters.
- Vowels: O, E
- Consonants: V, W, L, S
Total Arrangements Without Restrictions
First, calculate the total arrangements of the letters in "VOWELS".
- The total number of arrangements is 6! (factorial of 6) since all letters are distinct.
Calculating Total Arrangements
- Total arrangements = 6! = 720
Arrangements with All Consonants Together
Next, we treat the consonants (V, W, L, S) as a single unit. This changes our arrangement:
- New units: (VWLS), O, E
Now, we have 3 units: (VWLS), O, E.
Calculating Arrangements with Consonants Together
- The arrangements of these 3 units = 3! = 6
- The arrangements of the consonants within their unit = 4! = 24
Total With Consonants Together
- Total arrangements with consonants together = 3! * 4! = 6 * 24 = 144
Final Calculation
Now, to find the arrangements where the consonants do not come together:
- Arrangements where consonants do not come together = Total arrangements - Arrangements with consonants together
- = 720 - 144 = 576
Conclusion
The number of six-letter words formed from "VOWELS" such that all consonants never come together is 576.
To find the number of six-letter words formed from the letters of the word "VOWELS" such that all consonants do not come together, we start by identifying the letters.
- Vowels: O, E
- Consonants: V, W, L, S
Total Arrangements Without Restrictions
First, calculate the total arrangements of the letters in "VOWELS".
- The total number of arrangements is 6! (factorial of 6) since all letters are distinct.
Calculating Total Arrangements
- Total arrangements = 6! = 720
Arrangements with All Consonants Together
Next, we treat the consonants (V, W, L, S) as a single unit. This changes our arrangement:
- New units: (VWLS), O, E
Now, we have 3 units: (VWLS), O, E.
Calculating Arrangements with Consonants Together
- The arrangements of these 3 units = 3! = 6
- The arrangements of the consonants within their unit = 4! = 24
Total With Consonants Together
- Total arrangements with consonants together = 3! * 4! = 6 * 24 = 144
Final Calculation
Now, to find the arrangements where the consonants do not come together:
- Arrangements where consonants do not come together = Total arrangements - Arrangements with consonants together
- = 720 - 144 = 576
Conclusion
The number of six-letter words formed from "VOWELS" such that all consonants never come together is 576.
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The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is?
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The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is?.
The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is?.
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