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 4 of 10.
Gopika S S said:
10 years ago
A number of permutations of "n" different things are taken "m" specified things always come together is m!* (n-m+1) !
Here the three vowels always come together. So here m is 3. A total number of letters is 7. Substitute we get.
3!* (7 - 3 + 1)! = 3! * 5!
= 6 * 120 =720.
Hope you got it.
Here the three vowels always come together. So here m is 3. A total number of letters is 7. Substitute we get.
3!* (7 - 3 + 1)! = 3! * 5!
= 6 * 120 =720.
Hope you got it.
Jomson joy said:
10 years ago
In PACKET there are 2 vowels. Vowels came 2gether means 4! * 2! = 240.
Total words formed =6! (because of total letters) = 720.
Therefore 720 - 240 = 480.
Total words formed =6! (because of total letters) = 720.
Therefore 720 - 240 = 480.
KIRUPA RANI D said:
10 years ago
Can you give solution for this problem? How many words can be formed from the letters of the word 'PACKET', so that the vowels are never together?
Reshmi said:
4 weeks ago
Vowels in the word are EAI.
The remaining Letters are LDNG.
Since Vowels has to be together = 3!
Now consider EAI as a single letter and the remaining 4 letters altogether become 5 letters.
So 5!
Now we need to include all letters to make the word, hence 3! x 5! = 720.
The remaining Letters are LDNG.
Since Vowels has to be together = 3!
Now consider EAI as a single letter and the remaining 4 letters altogether become 5 letters.
So 5!
Now we need to include all letters to make the word, hence 3! x 5! = 720.
Technothelon said:
10 years 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.
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.
Shoba said:
2 decades ago
Other than vowels there are only 4 letter then how it s possible to get 5!.
Unnati Singh said:
3 months ago
I think the correct answer is 5040.
Pallavi said:
7 years ago
Why 120*6?
Why not 120+6? Please tell me the reason.
Why not 120+6? Please tell me the reason.
Aniket Arsad said:
7 years ago
Vowels are EA so _L_D_I_N_G_.
So there is six space we can arrange EA so the answer is 6! = 720.
So there is six space we can arrange EA so the answer is 6! = 720.
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