Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 2)
2.
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer: Option
Explanation:
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Video Explanation: https://youtu.be/WCEF3iW3H2c
Discussion:
97 comments Page 3 of 10.
A.Vamsi krishna said:
1 decade ago
"!" this implies factorial that means a number is multiplied
like for example take number 5 then its factorial will be
taken as 5*4*3*2*1 and this is equal to 120.
like for example take number 5 then its factorial will be
taken as 5*4*3*2*1 and this is equal to 120.
Santosh kumar pradhan said:
1 decade ago
Total member 7
out of which 5 consonant and 3 vowels
take 3 vowls as a 1
hen number of consonant will arrange 5! ways
and these 3 vowels will arrange 3! ways
though,5!*3!=720
out of which 5 consonant and 3 vowels
take 3 vowls as a 1
hen number of consonant will arrange 5! ways
and these 3 vowels will arrange 3! ways
though,5!*3!=720
Sowmya said:
9 years ago
@Xyz.
C,M,B,N,T,N,(O,I,A,I,O)=> C,M,B,T,N,(O,I,A)=> 6! ways.
Vowels alone can be rearranged themselves in 3! ways.
So 6! * 3! = 2160.
Hope this is right.
C,M,B,N,T,N,(O,I,A,I,O)=> C,M,B,T,N,(O,I,A)=> 6! ways.
Vowels alone can be rearranged themselves in 3! ways.
So 6! * 3! = 2160.
Hope this is right.
Soumya sengupta said:
10 years ago
If there is another vowel 'o' what should be done like in 'outstanding' here a, i, o, u are vowels do we have to consider (aiou) = 1 letter for calculation?
Jomson joy said:
9 years ago
In PACKET there are 2 vowels. Vowels came 2gether means 4! * 2! = 240.
Total words formed =6! (because of total letters) = 720.
Therefore 720 - 240 = 480.
Total words formed =6! (because of total letters) = 720.
Therefore 720 - 240 = 480.
KIRUPA RANI D said:
9 years ago
Can you give solution for this problem? How many words can be formed from the letters of the word 'PACKET', so that the vowels are never together?
Dhana said:
8 years ago
Word : leading
condition : vowels together
eai-3!
ldng&eai-5!
(ldng)&(eai)-2!
Whether the last condition is valid?
Give explanation.
condition : vowels together
eai-3!
ldng&eai-5!
(ldng)&(eai)-2!
Whether the last condition is valid?
Give explanation.
Othasekar said:
3 years ago
LEADING
Vowels can be together in 5 ways.
So 5!=120.
Vowels can be arranged in 3 ways.
So 3!=6.
Total = 120x6 = 720.
Hope you understand.
Vowels can be together in 5 ways.
So 5!=120.
Vowels can be arranged in 3 ways.
So 3!=6.
Total = 120x6 = 720.
Hope you understand.
(25)
Jon said:
8 years ago
@Tanmay.
SFTWR (OAE)
5 +(1) ! = 6!
OAE can be arranged in 3 ways 3!
6! = 6*5*4*3*2*1 = 720 ways
3! = 6 ways
720*6 = 4320 ways!
SFTWR (OAE)
5 +(1) ! = 6!
OAE can be arranged in 3 ways 3!
6! = 6*5*4*3*2*1 = 720 ways
3! = 6 ways
720*6 = 4320 ways!
Sai said:
1 decade ago
HI SHOBA,.
4 consonants + set of vowels (i. E. , L+N+D+G+ (EAI) ).
We should arrange all these 5. So we get 5!.
I think you understood.
4 consonants + set of vowels (i. E. , L+N+D+G+ (EAI) ).
We should arrange all these 5. So we get 5!.
I think you understood.
(1)
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