# 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 1 of 10.
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.

(15)

Ayush said:
3 years ago

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

(6)

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)

DHEEPAK S said:
3 years ago

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

(4)

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.

(22)

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)

Suraj said:
5 years ago

Make a queue of vowels should not come together.

(2)

Aradhy said:
5 years ago

@Deepanesh.

We are taking the possibilities of vowel because vowels can also change their position in the given arrangement.

We are taking the possibilities of vowel because vowels can also change their position in the given arrangement.

(1)

Deepanesh said:
5 years ago

Why we are taking possibilities of vowels too?

(1)

Ameena said:
5 years ago

Hello,

We have word leading.we have vowels( EAI), first taken as 1 and can be arranged in _L_D_N_G_ that is in 5! Ways, EAI in 3! Ways, and LNDG in 4! ways.

That is 5! * 4! * 3! = 17,280 ways.

We have word leading.we have vowels( EAI), first taken as 1 and can be arranged in _L_D_N_G_ that is in 5! Ways, EAI in 3! Ways, and LNDG in 4! ways.

That is 5! * 4! * 3! = 17,280 ways.

(5)

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