Q. 55.0( 1 Vote )

How many differen

Answer :

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


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