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?
360
480
720
5040
None of these
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 3 of 10.

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!

Tanmay said:   8 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:   8 years ago
I think it should be 3!*4!

Krishna said:   8 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.

Ali said:   8 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.

Avishek kadel said:   8 years ago
In how many ways the letters of word ELEMENT can be arranged so that vowels are always together?

Can anyone solve this?

Akshay said:   8 years ago
@Navan.

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.

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.

Juliana said:   7 years ago
How do you calculate combinations, can you do an example? Please.


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