Given, the word is ‘SUNDAY.’

To find: Number of words that can be formed using letters of the given word and number of words starting with D

Total number of letters in the word = 6

So, arrange these 6 letters

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 6 things taken all at a time

= P(6, 6)

{∵ 0! = 1}

= 6!

= 6 × 5 × 4 × 3 × 2 × 1

= 720

Hence, the total number of words can be made by letters of the word ‘SUNDAY’ = 720

Now, we need to find out a number of words starting with D

So, fix the position of first letter as D:

Remaining number of letters = 5

Now, arrange these 5 letters at 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 ‘SUNDAY’ starting with ‘D’ is 120