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Home » How many permutations can be formed by the letters of the word ‘VOWELS’, when (i) there is no restriction on letters; (ii) each word begins with E; (iii) each word begins with O and ends with L; (iv) all vowels come together; (v) all consonants come together?
How many permutations can be formed by the letters of the word ‘VOWELS’, when (i) there is no restriction on letters; (ii) each word begins with E; (iii) each word begins with O and ends with L; (iv) all vowels come together; (v) all consonants come together?
CBSE | Class 11 | Excercise 8D | Maths | Permutations | RS Aggarwal
How many permutations can be formed by the letters of the word ‘VOWELS’, when (i) there is no restriction on letters; (ii) each word begins with E; (iii) each word begins with O and ends with L; (iv) all vowels come together; (v) all consonants come together?

Answer : (i) There is no restriction on letters The word VOWELS contain 6 letters.

The permutation of letters of the word will be 6! = 720 words.

  • Each word begins with

Here the position of letter E is fixed.

Hence, the rest 5 letters can be arranged in 5! = 120 ways.

  • Each word begins with O and ends with L The position of O and L are

Hence the rest 4 letters can be arranged in 4! = 24 ways.

  • All vowels come together There are 2 vowels which are O, E. Consider this group.

Therefore, the permutation of 5 groups is 5! = 120

The group of vowels can also be arranged in 2! = 2 ways.

Hence the total number of words in which vowels come together are 120×2 = 240 words.

  • All consonants come together

There are 4 consonants V,W,L,S. consider this a group. Therefore, a permutation of 3 groups is 3! = 6 ways.

The group of consonants also can be arranged in 4! = 24 ways.

Hence, the total number of words in which consonants come together is 6×24 = 144 words.

 

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