how many arrangements can be formed by the letters of the word VOWELS if
1) All vowels come toghether, and,
2) All consonants come toghether.
no spams and plz answer kal exam hai thoda bahut doubt.s hai ba.s class 11 mathematics
Answers
Answer:
(i) The word VOWELS consists of 6 distinct letters that can be arranged amongst themselves in 6! ways.
∴ Number of words that can be formed with the letters of the word VOWELS, without any restriction = 6! = 720
1. The word VOWELS consists of 2 vowels.
If we keep all the vowels together, we have to consider them as a single entity.
Now, we are left with the 4 consonants and all the vowels that are taken together as a single entity.
This gives us a total of 5 entities that can be arranged in 5! ways.
It is also to be considered that the 2 vowels can be arranged in 2! ways amongst themselves.
By fundamental principle of counting:
∴ Total number of arrangements = 5!×2! = 240
2. The word VOWELS consists of 4 consonants.
If we keep all the consonants together, we have to consider them as a single entity.
Now, we are left with the 2 vowels and all the consonants that are taken together as a single entity.
This gives us a total of 3 entities that can be arranged in 3! ways.
It is also to be considered that the 4 consonants can be arranged in 4! ways amongst themselves