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 3 of 10.
Heta Vaghasia said:
9 years ago
Answer will be 72. How 720 came?
Vivek Sharma said:
9 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?
Nabin shah said:
9 years ago
Why do 120 and 6 multiply?
Dhana said:
9 years ago
Word : leading
condition : vowels together
eai-3!
ldng&eai-5!
(ldng)&(eai)-2!
Whether the last condition is valid?
Give explanation.
condition : vowels together
eai-3!
ldng&eai-5!
(ldng)&(eai)-2!
Whether the last condition is valid?
Give explanation.
Jon said:
9 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!
Tanmay said:
9 years ago
In how many different ways can the letters of the word software be arranged in such a way that the vowels always come together?
Abhishek said:
9 years ago
I think it should be 3!*4!
Krishna said:
9 years ago
LEADING- vowels together in total 5 positions at L, E, A, D, and I.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
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?
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