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.
Mahesh Babu said:
8 years ago
@ Simmie.
You did a mistake the correct procedure is;
Since no vowels come together, first arrange the 4 consonants in 4! ways.
Now, a vowel can be placed at the beginning of the consonants or at the end of the consonants or in between every two consonants.
_C_C_C_C_
They are 5 places to fill 3 vowels,
In these 5 places we can arrange the 3 vowels in 5!/2! ways(5p3 ways),
The number of words in which no vowels come together is,
4!*5!/2!=1440.
You did a mistake the correct procedure is;
Since no vowels come together, first arrange the 4 consonants in 4! ways.
Now, a vowel can be placed at the beginning of the consonants or at the end of the consonants or in between every two consonants.
_C_C_C_C_
They are 5 places to fill 3 vowels,
In these 5 places we can arrange the 3 vowels in 5!/2! ways(5p3 ways),
The number of words in which no vowels come together is,
4!*5!/2!=1440.
Simmie said:
8 years ago
@Sonam.
If non-vowels come together then,
Vowels OIA considering each as different units So its 3 units,
Non-vowels, PTCL as 1 units.
Its 4!=24 because they need to be arranged within themselves.
The vowels and non-vowels together they make 4 units..4!=24(its like consider "PTCL" as "x" ..now arranging them with vowels would be OIAX,OAIX,AIOX,IOAX,IAOX......i.e....4!)
So now,
Vowels and non-vowels = 4! = 24,
Non-vowels = 4! = 24,
24 * 24 = 576.
If non-vowels come together then,
Vowels OIA considering each as different units So its 3 units,
Non-vowels, PTCL as 1 units.
Its 4!=24 because they need to be arranged within themselves.
The vowels and non-vowels together they make 4 units..4!=24(its like consider "PTCL" as "x" ..now arranging them with vowels would be OIAX,OAIX,AIOX,IOAX,IAOX......i.e....4!)
So now,
Vowels and non-vowels = 4! = 24,
Non-vowels = 4! = 24,
24 * 24 = 576.
Shubham mishra said:
8 years ago
Yes, I too have same doubt @Anoushka.
Sonam said:
9 years ago
If the question is asked "no vowels come together" then what will be the answer?
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.
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).
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.
Mukesh said:
1 decade ago
Can we use the same method in question 13?
Anushq said:
1 decade ago
Hi all,
I have a doubt in questions regarding vowels and consonants. If we arrange all the vowels in one word, it can be in either consonant + (sum of vowels) or (sum of vowels) + consonant. Why all the answers are not considering the second option.
Because if we consider both the case then We need to multiply all the answers * 2. Please let me know if I am wrong.
I have a doubt in questions regarding vowels and consonants. If we arrange all the vowels in one word, it can be in either consonant + (sum of vowels) or (sum of vowels) + consonant. Why all the answers are not considering the second option.
Because if we consider both the case then We need to multiply all the answers * 2. Please let me know if I am wrong.
Navya said:
1 decade ago
Ibidun: A committee of 4 men and 2 women is selected from 10 men and 5 women. If 2 of the men are feuding and will not serve on the committee together, in how many ways can the committee be selected.
Sol: 5c2*9c3 ways.
Sol: 5c2*9c3 ways.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers