How many different ways can the letters of the word Leading be arranged such that the vowels should always come together?

  • Permutation and Combination - important notes
  • Permutation and Combination - General Questions

1. 

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?


2. 

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?


3. 

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?


4. 

In how many ways can the letters of the word 'LEADER' be arranged?


5. 

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?


3604807205040

Answer : C

Solution : The word 'LEADING ' has 7 different letters. <br> when the vowels EAI are always together , they can be supposed to form one letter. <br> then , we have to arrange the letters LNDG (EAI) . <br> 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. <br> `therefore ` Required number of ways `=(120 xx6)= 720`

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A. 360

B. 480

C. 720

D. 5040

E. None of these

Answer: Option C

Solution(By Examveda Team)

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.
Therefore Required number of ways = (120 x 6) = 720

How many different ways leading can be arranged so that vowels come together?

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! ... Permutation-and-Combination..

How many different way can the letters of the word Leading be arranged in such a way that the vowels always come together * A 360 B 480 C 720 D 5040?

= 120 ways. The vowels (EAI) can be arranged among themselves in 3!

How many different ways can the letters of the word Leading be arranged in such a way that the?

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: The correct answer is option (c) 720.

How many ways can the letter of the word mathematics be arranged so that the vowels always come together?

∴ Required number of words = (10080 x 12) = 120960.