Given:

The word ‘SUNDAY’

Total number of letters in the word ‘SUNDAY’ is 6.

So, number of arrangements of 6 things, taken all at a time is ^{6}P_{6}

= 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Now, we shall find the number of words starting with N

So let’s fix the first position with letter N, then remaining number of letters is 5.

The number of arrangements of 5 things, taken all at a time is ^{5}P_{5} = 5! = 5 × 4 × 3 × 2 × 1 = 120

Now, we need to find out a number of words starting with N and ending with Y

So let’s fix the first position with letter N and Y at the end, then remaining number of letters is 4 which can be arranged in ^{4}P_{4} ways. = 4! = 4 × 3 × 2 × 1 = 24

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

The possible number of words using letters of ‘SUNDAY’ starting with ‘N’ is 120.

The possible number of words using letters of ‘SUNDAY’ starting with ‘N’ and ending with ‘Y’ is 24.

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