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 4 of 4.
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.
Karan kumar said:
7 years ago
Vowels come together so there are 5!
And 3!.
120 * 6 = 720.
And 3!.
120 * 6 = 720.
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)
Rajeev said:
6 years ago
But the vowel can come in the beginning like;
OIAPTCL.
PTCLOIA.
So, we should add like this (5!*3!+5!*3!)
OIAPTCL.
PTCLOIA.
So, we should add like this (5!*3!+5!*3!)
(1)
Ayesha said:
6 years ago
OAI are 3 vowels should be considered as one letter (OAI) and the 3 vowels among themselves can be arranged in 3! ways ie.,6ways.
Now the remains consonants are PCTL are 4 letters plus we should consider the 3 vowels as one letter (4+1)=5! ways {5!=120}.
The required no.of ways = 120 * 6 =720 ways.
Now the remains consonants are PCTL are 4 letters plus we should consider the 3 vowels as one letter (4+1)=5! ways {5!=120}.
The required no.of ways = 120 * 6 =720 ways.
(3)
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)
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