How many different words can be formed with the letters of word ‘SUNDAY’? How many of the words begin with N? How many begin with N and end in Y?
Given: the word is ‘SUNDAY.’
To find: number of words that can be formed with the letters of the given word, that can begin with N, and that can begin with N and end in Y
Total number of letters = 6
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 of a number of words starting with N
So, fix the position of the first letter as N:
Remaining number of letters in the word ‘SUNDAY’ = 5
Now, we need to 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 ‘N’ is 120
Now, we need to find out a number of words starting with N and ending with Y
So, fix the position of first and last letter as N and Y:
Remaining number of letters = 4
Now, we need to arrange these 4 letters at 4 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 4 things taken all at a time
= P(4, 4)
{∵ 0! = 1}
= 4!
= 4 × 3 × 2 × 1
= 24
Hence, the possible number of words using letters of ‘SUNDAY’ starting with ‘N’ and ending with ‘Y’ are 24