Q. 235.0( 1 Vote )

How many permutat

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.


(ii) Each word begins with


Here the position of letter E is fixed.


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


(iii) Each word begins with O and ends with L


The position of O and L are fixed.


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


(iv) 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.


(v) 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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