Given: the word is ‘MONDAY.’

To find: possible number of words using all the letters of the word ‘MONDAY’ but the first letter is a vowel

Total number of vowels = 2(A, O)

Now, fix the position of 1 vowel out of these two at first place which can be done in 2 ways.

or

Now, we need to fill the remaining 5 places

Remaining places for letters = 5

So, arrange 5 letters at 5 places

Formula used:

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

∴ Total number of arrangements

= 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 total number of words can be made by using all letters of the word ‘MONDAY,’ but the first letter is vowel = 120 × 2 = 240