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With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is
- a)5780
- b)2890
- c)5440
- d)2720
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
With 17 consonants and 5 vowels the number of words of four letters th...
Solution:
Given, 17 consonants and 5 vowels.
Number of ways of selecting 2 different vowels from 5 is = 5C2 = 10.
Number of ways of selecting 1 consonant from 17 is = 17C1 = 17.
Number of ways of arranging the 3 selected letters = 3! = 6.
Therefore, the number of ways of forming a word of 4 letters having 2 different vowels in the middle and one consonant, repeated or different at each end is given by:
10 × 17 × 6 × 5 = 5100.
But in the above calculation, we have included the case where both the consonants are same i.e. repeated.
Therefore, the required number of ways of forming a word of 4 letters having 2 different vowels in the middle and one consonant, repeated or different at each end is:
= 5100 - (5 × 6 × 1) = 5780.
Hence, the correct option is (a) 5780.
Given, 17 consonants and 5 vowels.
Number of ways of selecting 2 different vowels from 5 is = 5C2 = 10.
Number of ways of selecting 1 consonant from 17 is = 17C1 = 17.
Number of ways of arranging the 3 selected letters = 3! = 6.
Therefore, the number of ways of forming a word of 4 letters having 2 different vowels in the middle and one consonant, repeated or different at each end is given by:
10 × 17 × 6 × 5 = 5100.
But in the above calculation, we have included the case where both the consonants are same i.e. repeated.
Therefore, the required number of ways of forming a word of 4 letters having 2 different vowels in the middle and one consonant, repeated or different at each end is:
= 5100 - (5 × 6 × 1) = 5780.
Hence, the correct option is (a) 5780.
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Community Answer
With 17 consonants and 5 vowels the number of words of four letters th...
The two letters, th e first and the last of the four lettered word can be chosen in (17)2 ways, as repetition is allowed for consonants. The two vowels in the middle are distinct so that the number of ways of filling up the two places is 5P2 = 20.
The no. of different words = (17)2 . 20 = 5780.
The no. of different words = (17)2 . 20 = 5780.
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With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end isa)5780b)2890c)5440d)2720Correct answer is option 'A'. Can you explain this answer?
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With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end isa)5780b)2890c)5440d)2720Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end isa)5780b)2890c)5440d)2720Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end isa)5780b)2890c)5440d)2720Correct answer is option 'A'. Can you explain this answer?.
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