Q. 1 C4.0( 2 Votes )

Find the number of words formed by permuting all the letters of the following words :

ARRANGE

Answer :

Since we know, Permutation of n objects taking r at a time is nPr,and permutation of n objects taking all at a time is n!


And, we also know Permutation of n objects taking all at a time having p objects of the same type, q objects of another type, r objects of another type is . i.e. the, number of repeated objects of same type are in denominator multiplication with factorial.


Given, the word ARRANGE. It has 7 letters, and it has 2 repeated letters ‘A’, ‘R.’ Of which, the letter A is repeated twice, and the letter R is also repeated twice. All other letters are distinct.


The problem can now be rephrased as to find a total number of permutations of 7 objects (A, R, R, A, N, G, E) of which two objects are of same type (A, A), and two objects are of another type (R, R).


Total number of such permutations



= 1260


Hence, a total number of permutations of the word ARRANGE is 1260.


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 CombinationsInteractive Quiz on CombinationsInteractive Quiz on Combinations50 mins
Division and distribution of objectsDivision and distribution of objectsDivision and distribution of objects58 mins
Interactive Quiz on Combinations-02Interactive Quiz on Combinations-02Interactive Quiz on Combinations-0253 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 :