-
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
Resources
-
Arts, Commerce & Sciences
Colleges
Upcoming Events
Resources
-
Management and Business Administration
Colleges & Courses
Predictors
-
Learn
Law Preparation
MBA Preparation
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
Exams
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 the second letter being N? <st
How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together and the second letter being N?
20
14
12
24
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 N, we can consider the placement of the R's and N separately.
Let's consider the placement of the two R's first. We have 6 entities to arrange: A, N, G, E, and two R's (R1 and R2). Since we want to ensure that the two R's are never together, we can think of placing the R's in alternate positions, creating a pattern like R_A_R_A.
There are three possible positions for the first R, and once it's placed, there are two possible positions for the second R.
Next, let's consider the placement of the second letter N. We have already placed the two R's, so there are four remaining positions for the N: _ N _ _.
Therefore, the number of ways to arrange the letters of "ARRANGE" such that the two R's are never together and the second letter is N is given by:
3 (positions for the first R) 2 (positions for the second R)
4 (positions for the second letter N) = 24.
Thus, there are 24 ways to arrange the letters of the word "ARRANGE" such that the two R's are never together, and the second letter is N.
JEE Main high-scoring chapters and topics
Study 40% syllabus and score up to 100% marks in JEE
