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 8 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!

Dhana said:   8 years ago
Word : leading
condition : vowels together
eai-3!
ldng&eai-5!
(ldng)&(eai)-2!

Whether the last condition is valid?
Give explanation.

Nabin shah said:   8 years ago
Why do 120 and 6 multiply?

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?

Heta Vaghasia said:   8 years ago
Answer will be 72. How 720 came?

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.

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

Saravanakumar said:   7 years ago
LEADING.

Total vowels : E , A, I
remaining : LDNG
assume : EAI we can arrange (EAI)L, L(EAI), D(EAI), N(EAI),G(EAI)

so, total remaining is 4 so, 5!
and possibilities of arranging refer "assume" , 3!
then answer is : 5!*3!
120 * 6=720.
(1)

Shivam said:   7 years ago
Why 120*6 why not 120+6? Please explain me.

Sankardev said:   7 years ago
-L-D-N-G.

5!/(5-3)! = 120/2=60.
60*3!=60*6,
=360.


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