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 1 of 6.

Avinash aswal said:   4 years ago
Here question says vowels occupy only the odd position, then what about consonants? Please clarify this.
(3)

Divya said:   5 years ago
@Devdp.

As per the question, Vowels can occupy only the odd position. But you have placed the vowel in even position. Explain clearly.
(5)

Dinesh S said:   6 years ago
DETAIL = vowels ( E A I) = 3!
No.of possible is(DETAIL)
_ _ _ _ _ _
1 2 3 4 5 6 letter so conditions is odd position only 1,3,5,place only possible....=3!
Then 3! x 3! = 36.
(4)

Omshiva said:   6 years ago
@Keshav.

By Using the Gauss method. The correct answer is A.
(6)

PREM said:   6 years ago
SIMPLE TRICK:

There are 6 Letters 3 V and 3 C.

6blank positions_ _ _ _ _ _.

Which can be filled like this VCVCVC.

3V3C2V2C1V1C = 3 * 3 * 2 * 2 * 1 * 1 = 36.
(22)

Sayani said:   6 years ago
If we can set the vowels in odd positions, we can get one combination like;

ED AT IL.

Like that;
So always one consonant comes along with a vowel.
So total combined words= 3!
And 3 vowels can arrange themselves in 3! -> Number Of ways.
So, total arrangement is= 3! *3!.
=36.

Sahana said:   6 years ago
We can arrange consonants in 3! ways in even position and 4 odd places can be occupied by 3 vowels in 4P3 ways.

So these can be arranged in 3!*4P3 =144 ways.

Am I right?
(1)

Navi said:   7 years ago
Simple:

(DTL) * (EAI).

(3*2*1) * (3*2*1).
(6)*(6) = 36.
(2)

Usha said:   7 years ago
Then what is the use of vowels arranged in odd position?

I think it's wrong.

Uthaya said:   7 years ago
@GANESH.

Management has 10 letters, so 10! = 3628800.

the letters m,a,n,e has repetition. So 10!/2!2!2!2! = 3628800/(2*2*2*2) = 226800.


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