Q. 35.0( 3 Votes )

How many words can be formed from the letters of the word ‘SUNDAY’? How many of these begin with D?

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


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutationsCircular permutationsCircular permutations61 mins
Challenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningFREE Class
Understand Permutations like never beforeUnderstand Permutations like never beforeUnderstand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Lecture on CombinationsLecture on CombinationsLecture on Combinations49 mins
Interactive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations-02Interactive Quiz on Combinations-02Interactive Quiz on Combinations-0253 mins
Interactive Quiz on CombinationsInteractive Quiz on CombinationsInteractive Quiz on Combinations50 mins
Division and distribution of objectsDivision and distribution of objectsDivision and distribution of objects58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :