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 8 of 10.
Bharti said:
1 decade ago
Thanks a lot. I had confusion before your explanations. Thanks a lot.
Mayur said:
1 decade ago
How it came like nPr formula and how you have solve it? please let me know.
Moaned said:
1 decade ago
I am not getting
Laxmikanth said:
1 decade ago
When should we take the one or more letters as a single unit and why?
Sachin Kumar said:
2 decades ago
Please make me understand this answer as did not get.
Riya said:
1 decade ago
@Tom and @Shantha.
Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination.
The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation.
Here, since the vowels EAI must always be together we consider it as a single word (EAI).
Thus, LDNG (EAI) make a 5 letter word.
It can be arranged in 5p5 ways = 5!ways.
Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI).
Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.
Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination.
The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation.
Here, since the vowels EAI must always be together we consider it as a single word (EAI).
Thus, LDNG (EAI) make a 5 letter word.
It can be arranged in 5p5 ways = 5!ways.
Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI).
Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.
Peter said:
10 years ago
If at least two vowels always together then what will be the answer for LEADING ?
Eswaru said:
10 years ago
Hey dude we have to form 7 letter words from LEADING that means we need to use all the letters at a time. So no repetition are allowed.
Mukesh said:
1 decade ago
Please anyone help me why repetition is not considered in the current problem?
Yonatan said:
1 decade ago
I can't understand the answer.
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