Q. 18

Mark the correct alternative in the following:

The number of arrangements of the letters of the word BHARAT taking 3 at a time is

A. 72

B. 120

C. 14

D. none of these.

Answer :

We have, 6 objects {B}, {H}, {A}, {R}, {A}, {T} and there are 2 A's.


So, the words can be formed out of the letters of the word ‘BHARAT’ taking 3 at a time can be done in 2 ways:


Case-1: When all the letters are distinct.


We have, 5 distinct letters, out of which taking three at a time, the number of words that can be formed = 5P3




= 60


Case-2: When 2 A’s are selected.


So, we have, 2A’s and 1 letter is to selected out of the 4 distinct letters, which can be done in = 4P1




= 4 ways.


Now, the 3 letters can be arranged among themselves, but there are 2 A’s, so the number of ways in which arrangement can be done is




So, in this case, total number of words that can be formed


= 12.


The number of arrangements of the letters of the word BHARAT taking 3 at a time is = (60 + 12)


= 72.

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 :