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?
32
48
36
60
120
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 6 of 6.

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?

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.

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.

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.

Divyansh said:   10 years ago
Brother only odd position so answer is 36.

Dev said:   10 years ago
It can be done by 6x5x4x3x2 divide by 2 and again divide by 10 = 36.

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.

Aditya said:   9 years ago
How can we solve the same question taking 'FATHER' as the given word?

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.


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