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In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
- a)36
- b)64
- c)120
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In how many different ways can the letters of the word DETAIL be arran...
There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3
= 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3
= 3! = 6.
Total number of ways = (6 x 6) = 36.
Most Upvoted Answer
In how many different ways can the letters of the word DETAIL be arran...
As there are sixwords I. detail so maximum probability is square of six that is 6^2 =36 which is the correct answer...
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Community Answer
In how many different ways can the letters of the word DETAIL be arran...
To solve this problem, we need to consider the following conditions:
1. The word is "DETAIL" which has 6 letters.
2. The vowels (E, A, I) must occupy only the odd positions.
3. The consonants (D, T, L) must occupy only the even positions.
To find the number of arrangements that satisfy these conditions, we can break down the problem into two parts:
1. Arranging the vowels (E, A, I) in the odd positions.
2. Arranging the consonants (D, T, L) in the even positions.
Arranging the vowels (E, A, I) in the odd positions:
Since there are 3 vowels and 3 odd positions (1st, 3rd, and 5th), we can arrange them in 3! = 6 ways.
Arranging the consonants (D, T, L) in the even positions:
Since there are 3 consonants and 3 even positions (2nd, 4th, and 6th), we can arrange them in 3! = 6 ways.
Total number of arrangements:
To find the total number of arrangements, we multiply the number of arrangements of vowels with the number of arrangements of consonants.
Total number of arrangements = 6 (vowels) * 6 (consonants) = 36
Hence, the correct answer is option A) 36.
1. The word is "DETAIL" which has 6 letters.
2. The vowels (E, A, I) must occupy only the odd positions.
3. The consonants (D, T, L) must occupy only the even positions.
To find the number of arrangements that satisfy these conditions, we can break down the problem into two parts:
1. Arranging the vowels (E, A, I) in the odd positions.
2. Arranging the consonants (D, T, L) in the even positions.
Arranging the vowels (E, A, I) in the odd positions:
Since there are 3 vowels and 3 odd positions (1st, 3rd, and 5th), we can arrange them in 3! = 6 ways.
Arranging the consonants (D, T, L) in the even positions:
Since there are 3 consonants and 3 even positions (2nd, 4th, and 6th), we can arrange them in 3! = 6 ways.
Total number of arrangements:
To find the total number of arrangements, we multiply the number of arrangements of vowels with the number of arrangements of consonants.
Total number of arrangements = 6 (vowels) * 6 (consonants) = 36
Hence, the correct answer is option A) 36.
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In how many different ways can the letters of the word DETAIL be arranged such that the vowels must occupy only the odd positions?a)36b)64c)120d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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