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:
98 comments Page 2 of 10.
Deepanesh said:
6 years ago
Why we are taking possibilities of vowels too?
(1)
Aradhy said:
6 years ago
@Deepanesh.
We are taking the possibilities of vowel because vowels can also change their position in the given arrangement.
We are taking the possibilities of vowel because vowels can also change their position in the given arrangement.
(1)
Sundar said:
1 decade ago
@Madhusudan
5! = 5 Factorial = 1 x 2 x 3 x 4 x 5 = 120
5! = 5 Factorial = 1 x 2 x 3 x 4 x 5 = 120
(1)
Madhusudan said:
1 decade ago
Could you kindly let me know what is ( ! ).Howe 5! = 120 ?
(1)
Subbu said:
2 decades ago
7!=5040
(1)
Sri said:
2 decades ago
As vowels are together take (EAI) as single letter i.e. , total no of letters are 5 (L, N, D, G, {EAI}).
No of ways can arrange these 5 letters are 5! ways.
Now we arranged 5 letters (L, N, D, G, {EAI}).
Next we have to arrange E, A, I (they may be EAI/EIA/AEI/AIE/IAE/IEA).
All these combinations imply that vowels are together.
So we have to multiply 5! and 3!.
No of ways can arrange these 5 letters are 5! ways.
Now we arranged 5 letters (L, N, D, G, {EAI}).
Next we have to arrange E, A, I (they may be EAI/EIA/AEI/AIE/IAE/IEA).
All these combinations imply that vowels are together.
So we have to multiply 5! and 3!.
(1)
Jessie said:
1 decade ago
7 letter word = LEADING
CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD
SO NO. OF WORDS = L,(EAI),D,N,G = 5
permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5!
0! is assumed to be 1!)
EAI can be arranged among each other in = nPr = 3!/(3-3)= 3!
hence 5! x 3! = 120 x 6 = 720
CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD
SO NO. OF WORDS = L,(EAI),D,N,G = 5
permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5!
0! is assumed to be 1!)
EAI can be arranged among each other in = nPr = 3!/(3-3)= 3!
hence 5! x 3! = 120 x 6 = 720
(1)
Tanmay said:
8 years ago
In how many different ways can the letters of the word software be arranged in such a way that the vowels always come together?
Abhishek said:
8 years ago
I think it should be 3!*4!
Krishna said:
9 years ago
LEADING- vowels together in total 5 positions at L, E, A, D, and I.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers