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.
Logesh said:
1 decade ago
How to find the rank of the word with possible combinations?
Pastor ThankGod Anyanwu said:
1 decade ago
How many different 10-member committees can be formed from the 100-members of the Nigeria Senate?
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.
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.
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
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/
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.
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
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
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}.
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