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Solve the following question and mark the best possible option.
How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonants
- a)23,760
- b)32,400
- c)17,280
- d)60,480
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Solve the following question and mark the best possible option.How man...
There are 3 vowels and 6 consonants with 2 N's among them. 2 vowels can be chosen in 3C2 = 3 ways.
If the word has 4 distinct consonants, these 4 consonants can be chosen in 5C4 = 5 ways.
If the consonants contain 2 N’s, the remaining 2 consonants can be chosen in 4C2 = 6 ways.
Once the vowels and consonants have been chosen. we can arrange these 6 letters in 6! = 720 ways. So, there are 3 x 720 x 5 = 10800 words that contain 4 distinct consonants and 3 x 6 x 720/2! = 6480 words that contain 2 N ’s.
Thus, the total number o f wrords is 10800 + 6480 = 17280.
Most Upvoted Answer
Solve the following question and mark the best possible option.How man...
Problem:
How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonants?
Solution:
To solve this problem, we can break it down into smaller steps and calculate the number of possibilities at each step.
Step 1: Count the number of vowels (V) and consonants (C) in the word HINDUSTAN.
- Vowels: I, U, A
- Consonants: H, N, D, S, T
Step 2: Choose 2 vowels out of the 3 available vowels.
- Number of ways to choose 2 vowels out of 3:
C(3,2) = 3! / (2!(3-2)!) = 3
Step 3: Choose 4 consonants out of the 5 available consonants.
- Number of ways to choose 4 consonants out of 5:
C(5,4) = 5! / (4!(5-4)!) = 5
Step 4: Arrange the chosen vowels and consonants in the 6-letter word.
- Number of ways to arrange the 2 vowels and 4 consonants in a 6-letter word:
6! / (2!4!) = 15
Step 5: Multiply the numbers of possibilities from each step to get the total number of six-letter words.
- Total number of six-letter words: 3 * 5 * 15 = 225
Conclusion:
The number of six-letter words that can be formed from the letters of the word HINDUSTAN, containing exactly 2 vowels and 4 consonants, is 225. Therefore, option C (17,280) is incorrect.
Correct answer:
The correct answer is option A (23,760).
How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonants?
Solution:
To solve this problem, we can break it down into smaller steps and calculate the number of possibilities at each step.
Step 1: Count the number of vowels (V) and consonants (C) in the word HINDUSTAN.
- Vowels: I, U, A
- Consonants: H, N, D, S, T
Step 2: Choose 2 vowels out of the 3 available vowels.
- Number of ways to choose 2 vowels out of 3:
C(3,2) = 3! / (2!(3-2)!) = 3
Step 3: Choose 4 consonants out of the 5 available consonants.
- Number of ways to choose 4 consonants out of 5:
C(5,4) = 5! / (4!(5-4)!) = 5
Step 4: Arrange the chosen vowels and consonants in the 6-letter word.
- Number of ways to arrange the 2 vowels and 4 consonants in a 6-letter word:
6! / (2!4!) = 15
Step 5: Multiply the numbers of possibilities from each step to get the total number of six-letter words.
- Total number of six-letter words: 3 * 5 * 15 = 225
Conclusion:
The number of six-letter words that can be formed from the letters of the word HINDUSTAN, containing exactly 2 vowels and 4 consonants, is 225. Therefore, option C (17,280) is incorrect.
Correct answer:
The correct answer is option A (23,760).
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Solve the following question and mark the best possible option.How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonantsa)23,760b)32,400c)17,280d)60,480Correct answer is option 'C'. Can you explain this answer?
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Solve the following question and mark the best possible option.How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonantsa)23,760b)32,400c)17,280d)60,480Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question and mark the best possible option.How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonantsa)23,760b)32,400c)17,280d)60,480Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question and mark the best possible option.How many six-letter words can be formed from the letters of the word HINDUSTAN so that the words contain exactly 2 vowels and 4 consonantsa)23,760b)32,400c)17,280d)60,480Correct answer is option 'C'. Can you explain this answer?.
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