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.
Santosh said:
1 decade ago
(1) In 7 letter word "OPTICAL" has 3 vowels. They are 'O','I' & 'A'. We can arrange them in 3! ways and the remaining 4 letters arranged in 4! ways.
(2) If we combine OIA, it occurs in 5 positions of entire lenght of the word.
(3) So, we have 5*3!*4! ways to arrange the given word/
(2) If we combine OIA, it occurs in 5 positions of entire lenght of the word.
(3) So, we have 5*3!*4! ways to arrange the given word/
Sandeepkumar said:
1 decade ago
(1) In letter OPTICAL there seven letters out of which 3 vowels and 4 consonants.
(2) If vowels are together they can be arranged among themselves in 3! ways.
(3) Now considering them as single term (1+4=5) they can be arranged among themselves in 5!ways
Total no.of ways=5!*3!=120*6=720
(2) If vowels are together they can be arranged among themselves in 3! ways.
(3) Now considering them as single term (1+4=5) they can be arranged among themselves in 5!ways
Total no.of ways=5!*3!=120*6=720
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.
Sugumaran said:
1 decade ago
@Jiyas.
Convert 30 min into sec, (i.e) 30*60=1800 sec.
Find the LCM of 2, 4, 6, 8, 10, 12=120.
That is every 120 seconds all the 6 bells are ringing together.
For 1800 sec=1800/120= 15 times.
Convert 30 min into sec, (i.e) 30*60=1800 sec.
Find the LCM of 2, 4, 6, 8, 10, 12=120.
That is every 120 seconds all the 6 bells are ringing together.
For 1800 sec=1800/120= 15 times.
Pastor ThankGod Anyanwu said:
1 decade ago
How many different 10-member committees can be formed from the 100-members of the Nigeria Senate?
Logesh said:
1 decade ago
How to find the rank of the word with possible combinations?
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.
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.
Mukesh said:
1 decade ago
Can we use the same method in question 13?
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.
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