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