- 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