Q. 35.0( 3 Votes )

How many words ca

Answer :

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


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