# 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:

97 comments Page 10 of 10.
Suraj said:
5 years ago

Make a queue of vowels should not come together.

(2)

Xyz said:
5 years ago

How many 5 letter words can be formed out of the word NATIONALIST?

How to solve this. Please help!

How to solve this. Please help!

(8)

Keerti AR said:
3 years ago

LEADING = 7 letters => 4 alphabets (LNDG) + 1 group (3 vowels) = 5 ! ways.

=>5 * 4 * 3 * 2 * 1 = 120.

Now, the group can be arranged in 3 ways, since there are 3 vowels,

So 3!=6 (3 * 2 * 1).

Hence, 120 * 6 = 720 ways can be arranged.

=>5 * 4 * 3 * 2 * 1 = 120.

Now, the group can be arranged in 3 ways, since there are 3 vowels,

So 3!=6 (3 * 2 * 1).

Hence, 120 * 6 = 720 ways can be arranged.

(25)

DHEEPAK S said:
3 years ago

I can't understand this, Please anyone help me to get it.

(4)

Sanjay Raj G said:
3 years ago

@All.

Answer is not 720.

Ans is 5040.

L E A D I N G

Total 7!

So 1*2*3*4*5*6*7 = 5040.

Answer is not 720.

Ans is 5040.

L E A D I N G

Total 7!

So 1*2*3*4*5*6*7 = 5040.

(6)

Ayush said:
3 years ago

Here 5! = 5*4*3*2*1 = 120.

(7)

Othasekar said:
2 years ago

LEADING

Vowels can be together in 5 ways.

So 5!=120.

Vowels can be arranged in 3 ways.

So 3!=6.

Total = 120x6 = 720.

Hope you understand.

Vowels can be together in 5 ways.

So 5!=120.

Vowels can be arranged in 3 ways.

So 3!=6.

Total = 120x6 = 720.

Hope you understand.

(18)

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