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 1 of 10.
Shoba said:
1 decade ago
Other than vowels there are only 4 letter then how it s possible to get 5!.
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.
Sachin Kumar said:
1 decade ago
Please make me understand this answer as did not get.
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!.
Subbu said:
1 decade ago
7!=5040
Madhusudan said:
1 decade ago
Could you kindly let me know what is ( ! ).Howe 5! = 120 ?
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
Laxmikanth said:
1 decade ago
When should we take the one or more letters as a single unit and why?
Moaned said:
1 decade ago
I am not getting
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
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