(i) How many different words can be formed with letters of the word ‘SUNDAY’ ? (ii)How many of the words begin with N? (iii)How many begin with N and end Y?

Explanation

The total number of letters in the word ‘SUNDAY’ is 6.
Therefore, number of arrangements of 6 things, taken all at a time is `\^6P_6`
`= (6! )= 6 xx 5 × 4 xx 3 xx 2 xx 1
= 720`

Then, we shall find the number of words starting with N ,now remaining number of letters is
`5_(P_5) = (5!) = 5 xx 4 xx 3 xx 2 xx 1
= 120`

Then, we need to find out a number of words starting with N and ending with Y
Therefore let’s fix the first position with letter N and Y at the end,
now remaining number of letters is 4 which can be arranged in `4_(P_4) `ways.
= `(4!) = 4 xx 3 xx 2 xx 1 = 24`

Thus, the total number of words can be made by letters of the word ‘SUNDAY’ is 720. Possible number of words using letters of ‘SUNDAY’ starting with ‘N’ is 120. Possible number of words using letters of ‘SUNDAY’ starting with ‘N’ and ending with ‘Y’ is 24.