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.

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/

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

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.

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.

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.

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.


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