Given: the word is ‘VOWELS.’

To find: number of words using letters of the given word starting with E

So, fix the position of the first letter as E:

Remaining number of letters = 5

Now, we need to arrange these 5 letters at the remaining 5 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 5 things taken all at a time

= P(5, 5)

{∵ 0! = 1}

= 5!

= 5 × 4 × 3 × 2 × 1

= 120

Hence, the possible number of words using letters of ‘VOWELS’ starting with ‘E’ is 120