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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is?
Most Upvoted Answer
The number of different words that can be formed with 12 consonants an...
Understanding the Problem
To find the total number of different words that can be formed using 12 consonants and 5 vowels by selecting 4 consonants and 3 vowels, we need to follow these steps:
Step 1: Selecting Consonants
- Choose 4 consonants from 12 available consonants.
- The number of ways to choose 4 consonants can be calculated using combinations.
Step 2: Selecting Vowels
- Choose 3 vowels from the 5 available vowels.
- Similarly, the number of ways to choose 3 vowels is calculated using combinations.
Step 3: Arranging the Chosen Letters
- After selecting the letters, we need to arrange the 7 letters (4 consonants + 3 vowels).
- The total arrangements can be calculated using the factorial of the total number of letters.
Calculations
- Selecting Consonants:
- The number of ways to choose 4 consonants from 12:
- C(12, 4) = 495
- Selecting Vowels:
- The number of ways to choose 3 vowels from 5:
- C(5, 3) = 10
- Arranging the Letters:
- The total arrangements of 7 letters:
- 7! = 5040
Total Number of Different Words
- Finally, multiply the results from the above steps:
- Total Words = C(12, 4) × C(5, 3) × 7!
- Total Words = 495 × 10 × 5040 = 24948000
Conclusion
The total number of different words that can be formed by taking 4 consonants and 3 vowels from the given letters is 24,948,000.
To find the total number of different words that can be formed using 12 consonants and 5 vowels by selecting 4 consonants and 3 vowels, we need to follow these steps:
Step 1: Selecting Consonants
- Choose 4 consonants from 12 available consonants.
- The number of ways to choose 4 consonants can be calculated using combinations.
Step 2: Selecting Vowels
- Choose 3 vowels from the 5 available vowels.
- Similarly, the number of ways to choose 3 vowels is calculated using combinations.
Step 3: Arranging the Chosen Letters
- After selecting the letters, we need to arrange the 7 letters (4 consonants + 3 vowels).
- The total arrangements can be calculated using the factorial of the total number of letters.
Calculations
- Selecting Consonants:
- The number of ways to choose 4 consonants from 12:
- C(12, 4) = 495
- Selecting Vowels:
- The number of ways to choose 3 vowels from 5:
- C(5, 3) = 10
- Arranging the Letters:
- The total arrangements of 7 letters:
- 7! = 5040
Total Number of Different Words
- Finally, multiply the results from the above steps:
- Total Words = C(12, 4) × C(5, 3) × 7!
- Total Words = 495 × 10 × 5040 = 24948000
Conclusion
The total number of different words that can be formed by taking 4 consonants and 3 vowels from the given letters is 24,948,000.
Community Answer
The number of different words that can be formed with 12 consonants an...
12c4×5c3
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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is?
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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is?.
The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is?.
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