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 1 of 4.

Kishore said:   1 decade ago
Can you please brief me about 5!letters = 120 ways and 3! = 6 ways

Chandu said:   1 decade ago
@Kishore

5!=5*4*3*2*1=120
3!=3*2*1=6

Praveen said:   1 decade ago
There are 4 letters in this, so we can arrange those 4 letters in 4!ways and not in 5! ways..

Now, 4 letters can be arranged in 4!=24

The vowels (OIA) can be arranged among themselves in 3!=6 ways

Required number of ways =(24*6)=144

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 ?

Gayathri said:   1 decade ago
There are only 4! non vowels letter present can please tell me how you did with 5 !

Amogha said:   1 decade ago
Take the vowels as 1 unit and non-vowels, each as 1 unit.

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}.

ACHUTHARAJ said:   1 decade ago
Ya mini is correct

P+T+C+L+(OIA)= 5!=5X4X3X2X1=120
OIA =3!=3X2X1=6
120*6=720

Naveen said:   1 decade ago
5!=5*4*3*2*1=120
3!=3*2*1=6
120*6=720

Ibidun said:   1 decade ago
Please can some please help in solving this with explanation.

(1) 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.

(2) In how many ways can a football team be selected from 15 players? IN how many ways if 6 particular players must be included in the team.


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