# 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
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

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.

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.
(22)

Xyz said:   5 years ago
How many 5 letter words can be formed out of the word NATIONALIST?

(8)

Suraj said:   5 years ago
Make a queue of vowels should not come together.
(2)

@Deepanesh.

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.
(5)