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 3 of 10.
Ali said:
9 years ago
@Avishek
No. of vowels is 3Es and the can only be together in this pattern {EEE}. There is only 1 way of choosing so 1! = 1 * 1 = 1.
We are to consider 3Es as a single alphabet because they are together. So we have L, M, N, T,{EEE} ie 5 letters now in all.
Now of way of choosing 5 letters = 5! (5 * 4 * 3 * 2 * 1) = 120.
Finally, we multiply 120 * 1 = 120 ie. the number of ways of arranging the letters so that the vowels are always together.
No. of vowels is 3Es and the can only be together in this pattern {EEE}. There is only 1 way of choosing so 1! = 1 * 1 = 1.
We are to consider 3Es as a single alphabet because they are together. So we have L, M, N, T,{EEE} ie 5 letters now in all.
Now of way of choosing 5 letters = 5! (5 * 4 * 3 * 2 * 1) = 120.
Finally, we multiply 120 * 1 = 120 ie. the number of ways of arranging the letters so that the vowels are always together.
Avishek kadel said:
9 years ago
In how many ways the letters of word ELEMENT can be arranged so that vowels are always together?
Can anyone solve this?
Can anyone solve this?
Akshay said:
9 years ago
@Navan.
15c11 = 15!&div(15-11)! * 11!
15c11 = 15!&div(15-11)! * 11!
Navan said:
9 years ago
I have one question.
How many ways 11players selected from 15 players?
Please give me the answer.
How many ways 11players selected from 15 players?
Please give me the answer.
Brian said:
10 years 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
Sowmya said:
9 years ago
@Xyz.
C,M,B,N,T,N,(O,I,A,I,O)=> C,M,B,T,N,(O,I,A)=> 6! ways.
Vowels alone can be rearranged themselves in 3! ways.
So 6! * 3! = 2160.
Hope this is right.
C,M,B,N,T,N,(O,I,A,I,O)=> C,M,B,T,N,(O,I,A)=> 6! ways.
Vowels alone can be rearranged themselves in 3! ways.
So 6! * 3! = 2160.
Hope this is right.
Xyz said:
9 years ago
How many letters can be formed from COMBINATION if vowels are kept together?
Please give the solution.
Please give the solution.
Otieno said:
9 years ago
Where has 5! come from? Please explain me.
Rakesh said:
9 years ago
In leading 5! * 3! ways we can fill all vowels come together.
Prajwal said:
9 years ago
Does it have an another method to find the solution?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers