Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 10)
10.
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
Answer: Option
Explanation:
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, 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.
Discussion:
59 comments Page 2 of 6.
Vasudha said:
1 decade ago
Since there is nothing mentioned about repetitions so the no ways could also be 3*3*3(i.e., E can come in all three odd places and same goes for the other two vowels A and I as well) for the three odd positions of vowels.
And similarly the other three letters can be arranged so the answer should be 3*3*3*3*3*3.
And similarly the other three letters can be arranged so the answer should be 3*3*3*3*3*3.
Sanjay said:
1 decade ago
Hi guys.
There is 3 odd, 3 even place and the word have 3 vowel and 3consonant. We arrenge 3 vowel in 3 odd place and 3 consonant in 3 rest place such that VCVCVC So total no of way = 3p3*3p3 = 36.
There is 3 odd, 3 even place and the word have 3 vowel and 3consonant. We arrenge 3 vowel in 3 odd place and 3 consonant in 3 rest place such that VCVCVC So total no of way = 3p3*3p3 = 36.
Neha pant said:
1 decade ago
But here it is not mentioned that repetition is allowed so according to me the correct way is,
3*3*3*3*3*3 = 729 which is not in option.
3*3*3 for 3 vowels and other for consonant .
Please explain it?
3*3*3*3*3*3 = 729 which is not in option.
3*3*3 for 3 vowels and other for consonant .
Please explain it?
Nee said:
1 decade ago
Can't we do it in this way like first we find all possible ways of arranging all letters.
i.e 6! and then subtract 4!(3!) from 6! to get the answer.
i.e 6! and then subtract 4!(3!) from 6! to get the answer.
Priya said:
1 decade ago
Any example of cards combination. Tell me.
PRAKASH S said:
1 decade ago
I really don't understand why we are doing that.
How we are taken 3p3 = 6?
How we are taken 3p3 = 6?
Rohini said:
1 decade ago
Why write this type 3p3?
Subhadeep said:
10 years ago
We can consider the seventh position also. So I feel the answer is wrong.
Raji said:
10 years ago
I think we arrange 3 consonants + 1 vowel = 4 (generally 3 vowels but total vowels take as 1 set).
So 4! = 12.
The three vowels re arrange is 3!=6. So answer is 72.
Is there any wrong, please tell me.
So 4! = 12.
The three vowels re arrange is 3!=6. So answer is 72.
Is there any wrong, please tell me.
Sourav Sarkar said:
10 years ago
Well, there are four odd positions according to me.
1234567.
1, 3, 5, 7 are the odd positions.
3 vowels have to be selected to fit in any of the three position out of four.
This can be done in 4C3 ways. The rest remains the same.
Answer- 4C3x3!x3!
1234567.
1, 3, 5, 7 are the odd positions.
3 vowels have to be selected to fit in any of the three position out of four.
This can be done in 4C3 ways. The rest remains the same.
Answer- 4C3x3!x3!
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