Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 14)
14.
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
120
720
4320
2160
None of these
Answer: Option
Explanation:

The word 'OPTICAL' contains 7 different letters.

When the vowels OIA are always together, they can be supposed to form one letter.

Then, we have to arrange the letters PTCL (OIA).

Now, 5 letters can be arranged in 5! = 120 ways.

The vowels (OIA) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

Discussion:
36 comments Page 2 of 4.

B.madhan said:   10 years ago
It is very simple.

Given that vowels are come together means = All vowels are comes one place.

Means the word OPTICAL = OIA = 3! = 6 = vowels.

Constants = PTCL = 4! = 24.

(24*6 = 144).

Aswin kumar said:   1 decade ago
Can any one please tell me where do you get problems on circular combination and permutations. Ex: like number of ways for arranging people in round table conference. Something like that.

Mini said:   1 decade ago
@GAYATRI
After considering vowels as 1 set, remaning consonants and the vowel set => P+T+C+L+(0IA) => 5 letters {because we hav to consider that the vowels always come together}.

Jiyas said:   1 decade ago
6 bells comments talling together &tall at the intervels of 2,4,6,8,10,&12 second respectively.

In 30 minits how many time do they tall together ?

Gaurav said:   7 years ago
Short trick of that question is;

Total letters=7!,
Total vowels=3!(or 1group),
7!-3!=4!,
4!+1!(group of vowel)=5!,
Num of ways=5!*3!=720 is the answer.

Justice said:   3 years ago
Can you solve this "in how many different ways can the letters of the word "OPTICAL" be arranged.

So that O&A can always be together.
(1)

Anoushka said:   9 years ago
Sir I haven't understood why are we taking 5. Instead of 5 we should take 4. As in previous questions also we were taking 8 and not 9.

Shanmukh said:   1 decade ago
Hi Anushq,

We consider consonants + (sum of vowels) because in the question he mentioned that all vowels must be kept together.

Pudi sai kumar said:   7 years ago
Different ways of arranging the word "EASYQUIZ" where vowels always come together.

Can anyone solve this clearly?
(1)

Thaslim said:   8 years ago
When order takes important place then it is a permutation.

In Combination, order doesn't play an important role.


Post your comments here:

Your comments will be displayed after verification.