Q. 1 I5.0( 1 Vote )

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

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 CONSTANTINOPLE. It has 14 letters and it has 3 repeated letters ‘O’, ‘N,’ and ‘T.’ The letter O is repeated twice, the letter N is repeated thrice, and letter T is repeated twice. And all other letters are distinct.

The problem can now be rephrased as to find total number of permutations of 14 objects (C, O, N, S, T, A, N, T, I, N, O, P, L, E) of which two objects are of same type (O, O), three objects are of another type (N, N, N), and the two objects are of different type (T, T).

Total number of such permutations

= 3632428750

Hence, total number of permutations of the word CONSTANTINOPLE is 3632428750.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never before60 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division 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
view all courses