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:
99 comments Page 9 of 10.
Technothelon said:
1 decade ago
@Brian.
There aren't such kind of ways. Because arrangement is not taken into consideration when we do combinations.
There aren't such kind of ways. Because arrangement is not taken into consideration when we do combinations.
Brian said:
1 decade ago
Correct me if I'm wrong but,
There are 7 letters:
L E A D I N G
3 vowels and 5 non-vowels.
I got the part where we need to permutate 3 and 5, resulting with 3!*5!. But aren't there also several other positions that these vowels could be positioned?
For Example:
AIELDNG is one factor, another factor is LAIEDNG, another factor is LDAIENG.
As you can see, the positions of the 3 vowels with each other are the same, and the order of non-vowels in the word is also the same, but I only changed the position of the starting point for the vowel permutations, starting from the first position, to the second, to the third. So, I believe that the answer should be 3!*5!*5. Since there are 5 different ways you could represent the same order of vowels in different positions with the same order of non-vowels.
Please do correct me if I'm wrong or if I misunderstood the question
There are 7 letters:
L E A D I N G
3 vowels and 5 non-vowels.
I got the part where we need to permutate 3 and 5, resulting with 3!*5!. But aren't there also several other positions that these vowels could be positioned?
For Example:
AIELDNG is one factor, another factor is LAIEDNG, another factor is LDAIENG.
As you can see, the positions of the 3 vowels with each other are the same, and the order of non-vowels in the word is also the same, but I only changed the position of the starting point for the vowel permutations, starting from the first position, to the second, to the third. So, I believe that the answer should be 3!*5!*5. Since there are 5 different ways you could represent the same order of vowels in different positions with the same order of non-vowels.
Please do correct me if I'm wrong or if I misunderstood the question
Siva said:
1 decade ago
Other than vowels there are only 4 letter then how it s possible to get 5!.
Peter said:
1 decade ago
If at least two vowels always together then what will be the answer for LEADING ?
Eswaru said:
1 decade 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.
Palak said:
1 decade ago
In this question won't the arrangement of non vowels matter and why?
RAJA said:
1 decade ago
Hai @Soumya.
S its 1 letter only. Hope you understand.
S its 1 letter only. Hope you understand.
Shiva said:
1 decade ago
Why we have taken 5 (4 + 1) ?
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