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 4 of 6.
M223 said:
9 years ago
How many ways can the word DETAIL be rearranged such that no two vowels are placed adjacently?
Please tell me the answer.
Please tell me the answer.
Aditya said:
9 years ago
How can we solve the same question taking 'FATHER' as the given word?
Pinky kumari said:
9 years ago
The answer will be 36. It is correct. Because there is 3 odd place for vowel and 3 for a consonant.
Dev said:
10 years ago
It can be done by 6x5x4x3x2 divide by 2 and again divide by 10 = 36.
Divyansh said:
10 years ago
Brother only odd position so answer is 36.
Devdp said:
10 years ago
In 3rd line permutation for why 3p3 = 3! = 6.
This small mistake done bye me in writing but answer I got is 72.
Reply anyone.
This small mistake done bye me in writing but answer I got is 72.
Reply anyone.
Devdp said:
10 years ago
When 1st try myself consider x vowel and y consonants it can be possibility of position (1) xyxyxy and (2) yxyxyx.
As per permutation for x 3p3 = 3! = 6.
Permutation for why 3y3 = 3! = 6.
And as shown as above 2 different position.
Total arrangement = 6*6*2 = 72 (Ans).
But when I shows option I confused. There is no 72.
As per permutation for x 3p3 = 3! = 6.
Permutation for why 3y3 = 3! = 6.
And as shown as above 2 different position.
Total arrangement = 6*6*2 = 72 (Ans).
But when I shows option I confused. There is no 72.
Balakrishna said:
1 decade ago
Here they didn't mention about repetition allowed or not if we do this problem with repetition allowed the answer may be not 36.
Shivam said:
1 decade ago
There are 4 possible position for the vowel so why 4C3 is not included in the solution for selecting 3 position out of 4 for vowels?
Sourav Sarkar said:
1 decade 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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