Q. 165.0( 1 Vote )

# How many different arrangements can be made by using all the letters in the word ‘MATHEMATICS.’ How many of them begin with C? How many of them begin with T?

Given the word MATHEMATICS. It has 11 letters of which the letters M, A, and T are repeating and all letters are repeated twice.

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 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.

Total number of permutations of 11 objects with 3 objects repeating twice

= 4989600

To find the number of words starting with the letter C: This will be equal to permutation of 10 letters (excluded the letter C) where 3 letters (M, A, and T) are repeated twice

= 453600

To find the number of words starting with the letter T: This will be equal to permutation of 10 letters (excluded the letter T) where 2 letters (M, A) are repeated twice, which will be equals to

= 907200

Hence, a total number of words permuting the letters of word MATHEMATICS is 4989600. A total number of words starting with the letter C is 453600. A total number of words starting with the letter T equals 907200.

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
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Interactive 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
view all courses