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 5 of 10.
Kiran kumar k said:
7 years ago
How you get 5(4+1=5) i.e 5!?
Pooja said:
7 years ago
5! means? Explain
Tushar said:
7 years ago
@Shiva.
It means 5!.
It means 5!.
Supriya said:
8 years ago
LEADING- V-3,(1 unit).
C-4 ,(4+ 1unit)=5!
n-7.
=5!*3!=120*6=720.
C-4 ,(4+ 1unit)=5!
n-7.
=5!*3!=120*6=720.
Jon said:
8 years ago
@Tanmay.
SFTWR (OAE)
5 +(1) ! = 6!
OAE can be arranged in 3 ways 3!
6! = 6*5*4*3*2*1 = 720 ways
3! = 6 ways
720*6 = 4320 ways!
SFTWR (OAE)
5 +(1) ! = 6!
OAE can be arranged in 3 ways 3!
6! = 6*5*4*3*2*1 = 720 ways
3! = 6 ways
720*6 = 4320 ways!
Shivam said:
8 years ago
Why 120*6 why not 120+6? Please explain me.
Juliana said:
8 years ago
How do you calculate combinations, can you do an example? Please.
DragonSlayer said:
8 years ago
Friends in the word LEADING.
there are three vowels A,E,I
With AEI you can form 3! arrangements ie 6 arrangements
As we want the vowels to come together they may be placed at any of the 5 locations on the word LEADING.
So there are 5! arrangements for this.
5! X 3!=720.
The 3 vowels are considered as a single word to simply this process of counting the number if locations.
there are three vowels A,E,I
With AEI you can form 3! arrangements ie 6 arrangements
As we want the vowels to come together they may be placed at any of the 5 locations on the word LEADING.
So there are 5! arrangements for this.
5! X 3!=720.
The 3 vowels are considered as a single word to simply this process of counting the number if locations.
Heta Vaghasia said:
8 years ago
Answer will be 72. How 720 came?
Vivek Sharma said:
8 years ago
It should be 1440, as the vowels can be after the consonants as well as before the consonants. So 720*2. Am I right?
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