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 10 of 10.
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:
1 decade ago
7!=5040
(1)
Sri said:
1 decade 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)
Sachin Kumar said:
1 decade ago
Please make me understand this answer as did not get.
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)
Shoba said:
1 decade ago
Other than vowels there are only 4 letter then how it s possible to get 5!.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers