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