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 3 of 4.
Chandu said:
2 decades ago
@Kishore
5!=5*4*3*2*1=120
3!=3*2*1=6
5!=5*4*3*2*1=120
3!=3*2*1=6
Praveen said:
2 decades 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
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
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}.
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
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
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.
(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.
Kishore said:
2 decades ago
Can you please brief me about 5!letters = 120 ways and 3! = 6 ways
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
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