-
Engineering and Architecture
Exams
Colleges
Predictors
Resources
-
Computer Application and IT
Quick Links
Colleges
-
Pharmacy
Colleges
Resources
-
Hospitality and Tourism
Colleges
Resources
Diploma Colleges
-
Competition
Other Exams
Resources
-
School
Exams
Top Schools
Products & Resources
-
Study Abroad
Top Countries
Student Visas
-
Arts, Commerce & Sciences
Exams
Colleges
Upcoming Events
Resources
-
Management and Business Administration
Colleges & Courses
Predictors
-
Learn
Online Courses
Engineering Preparation
Medical Preparation
-
Online Courses and Certifications
Top Streams
Specializations
- Digital Marketing Certification Courses
- Cyber Security Certification Courses
- Artificial Intelligence Certification Courses
- Business Analytics Certification Courses
- Data Science Certification Courses
- Cloud Computing Certification Courses
- Machine Learning Certification Courses
- View All Certification Courses
Resources
-
Medicine and Allied Sciences
Colleges
Predictors
Resources
-
Law
Resources
Colleges
-
Animation and Design
Predictors & Articles
Colleges
Resources
-
Media, Mass Communication and Journalism
Colleges
Resources
-
Finance & Accounts
Top Courses & Careers
Colleges
Get Answers to all your Questions
- Home
- Engineering
- How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together and second letter being R?Option: 1</stron
How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together and second letter being R?
640
660
400
800
Answers (1)
To calculate the number of ways the letters of the word "ARRANGE" can be arranged such that the two R's are never together and the second letter is R, we can consider the placement of the R's and the second letter separately.
Let's consider the placement of the two R's first. We have 6 entities to arrange: A, R, G, A, N, and E. Since we want to ensure that the two R's are never together, we need to find the number of arrangements where the R's are not adjacent.
To calculate this, we can use the principle of complementary counting. The total number of arrangements without any restrictions is given by .
Now, let's count the number of arrangements where the two R's are adjacent. We can treat the two R's as a single entity, denoted as (RR). This means we have 5 entities to arrange: A, (RR), G, A, N, and E. Within this arrangement, the two A's are repeated, so we divide by .
The number of arrangements with the two R's adjacent is then .
To calculate the number of arrangements where the two R's are never together, we subtract the number of arrangements with the two R's adjacent from the total number of arrangements:
.
Calculating this expression, we have:
.
Thus, there are 660 ways to arrange the letters of the word "ARRANGE" such that the two R's are never together and the second letter is R.
JEE Main high-scoring chapters and topics
Study 40% syllabus and score up to 100% marks in JEE
