Question

How many permutations can be formed by the letters of the word, ‘VOWELS,’ when ach word begins with O and ends with L?

Answer 1

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 : 

O

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)

P(n, r) = \(\frac{n!}{(n-r)!}\) 

∴ The total number of ways 

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

= P(4, 4)

= \(\frac{4!}{(4-4)!}\) 

= \(\frac{4!}{0!}\)

{∵ 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.