Q. 7 C5.0( 2 Votes )

How many permutations can be formed by the letters of the word, ‘VOWELS,’ when

ach word begins with O and ends with L?

Answer :

Given: the word is ‘VOWELS.’


To find: number of words using letters of the given word starting with O and ending with L


So, fix the position of first and last letter as O and L:



Remaining number of letters = 4


Now, we need to arrange these 4 letters at the remaining 4 places.


Formula used:


Number of arrangements of n things taken all at a time = P(n, n)



The total number of ways


= the number of arrangements of 4 things taken all at a time


= P(4, 4)




{ 0! = 1}


= 4!


= 4 × 3 × 2 × 1


= 24


Hence, the possible number of words using letters of ‘VOWELS’ starting with ‘O’ and ending with ‘L’ is 24


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