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.

Gayathri said:   1 decade ago
Why we use permutation concept instead of combination.

Manasa said:   1 decade ago
@Gayathri

In this case we are not selecting any letters. Just we are arranging the letters according to given condition.

Kesav said:   1 decade ago
Can any one solve this problem for me?

1! + 2! + .... + 50!=?

a) 3.1035*10^64
b) 2.1021*10^65
c) 3.1035*10^63
d) 3.1035*10^62

Riddhi said:   1 decade ago
@kesav:plz give me ans. Is it b?

Vishnu said:   1 decade ago
It is asked in TCS apti test.

Gautam said:   1 decade ago
There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Number of ways of arranging the vowels = nPr= n!/(n-r)= 3/(3-3)
=3!/0! ,=3*2*1= 6 {we define 0! = 1}

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of arranging the vowels = nPr= n!/(n-r)= 3/(3-3)
=3!/0! ,=3*2*1= 6 {we define 0! = 1}.

Total number of ways = (6 x 6) = 36.

Nikhil said:   1 decade ago
Vowel can even be put at the 7th place, not considered above, which will increase the number of possible arrangements. Please clarify?

Athu said:   1 decade ago
What is odd positions?

Drushya said:   1 decade ago
@Athu.

Odd position means its like odd no.

For example : 1 2 3 4 5 6.

In this case odd position is :1 3 5 & even position : 2 4 6.

Jinal said:   1 decade ago
Vowels can also take position 7 (the last position) ?

V C V C V C V.

So the answer would be 3!*4C3 = 24.

Is this correct?


Post your comments here:

Your comments will be displayed after verification.