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 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.

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

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/

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.

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

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}.


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