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 8 of 10.
Chetas said:
1 decade ago
@Adhityasena.
You have not considered a vowel 'I'. 'EAI' is to be taken as one unit.
You have not considered a vowel 'I'. 'EAI' is to be taken as one unit.
Adhityasena said:
1 decade ago
I get the answer to be 2*720. Because, since the vowels must come together in the word LEADING, which actually has 7 letters, E and A can be taken as one unit, so now we have L, EA, D, I, N, G to be arranged and which can be done in 6! ways. But among E and A there are 2 arrangements namely EA and AE, So the final answer is 2*720. Am I right !
Shafi said:
1 decade ago
@Mahantesh,
You are correct 3! and 4!, because you spitted vowels and consonants,
But to combine them vowels+consonants.
i.e. (4 consonants + 1 set of vowels) = 5!
And (3 vowels {1 set}) = 3!
So 5!*3! = 5x4x3x2x1x3x2x1=720.
You are correct 3! and 4!, because you spitted vowels and consonants,
But to combine them vowels+consonants.
i.e. (4 consonants + 1 set of vowels) = 5!
And (3 vowels {1 set}) = 3!
So 5!*3! = 5x4x3x2x1x3x2x1=720.
Srk said:
1 decade ago
@Mahantesh.
1. There is given a word LEADING in this LDNG (consonents) , EAI (vowels).
2. They asked here vowels always come together and so we should have to take LDNG (EAI).
3. We can take as (4+1) ! i.e. here we have to take vowels as together as 1. So we have a chance of 5!.
4. But with in vowels we have many arrangements i.e 3!
5. Finally 5!*3!
1. There is given a word LEADING in this LDNG (consonents) , EAI (vowels).
2. They asked here vowels always come together and so we should have to take LDNG (EAI).
3. We can take as (4+1) ! i.e. here we have to take vowels as together as 1. So we have a chance of 5!.
4. But with in vowels we have many arrangements i.e 3!
5. Finally 5!*3!
Sandeep said:
1 decade ago
can any one explain ? y 5!*3! & y not like this 5!+3!
Mahanthesh said:
1 decade ago
Hi guys. As per the question, it s mentioned that all vowels should be together, but it has not been mentioned that it should be EAI. According to me these 3 vowels can be arranged in 3*2=6 ways. And the remaining letters LDNG can be arranged in 4*3*2*1= 24 ways. Can anyone explain me about this please ?
Raj said:
1 decade ago
Friends, How do you say this question is permutation.
Ncs said:
1 decade ago
Why not 5! + 3! ?
A.Vamsi krishna said:
1 decade ago
"!" this implies factorial that means a number is multiplied
like for example take number 5 then its factorial will be
taken as 5*4*3*2*1 and this is equal to 120.
like for example take number 5 then its factorial will be
taken as 5*4*3*2*1 and this is equal to 120.
Sagar choudhary said:
1 decade ago
What is this 5! and 3! ?
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