-
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
Exams
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
- A committee of 6 people needs to be formed from a group of 15 individuals, including 8 men and 7 women. If the committee must have an equal number of men and women, and a specific man refuses to se
A committee of 6 people needs to be formed from a group of 15 individuals, including 8 men and 7 women. If the committee must have an equal number of men and women, and a specific man refuses to serve together with a specific woman, how many different committees can be formed?
600
400
900
700
Answers (1)
To calculate the number of different committees that can be formed from a group of 15 individuals, including 8 men and 7 women, with the condition that the committee must have an equal number of men and women and a specific man refuses to serve together with a specific woman, we can consider the following:
We need to choose 3 men and 3 women to form the committee. Since a specific man and woman cannot serve together, we need to exclude this pair from the selection.
To calculate the number of ways to choose 3 men out of the remaining 7 men (excluding the specific man) and 3 women out of the 6 women (excluding the specific woman), we use the combination formula.
The number of ways to choose 3 men from 7 is , and the number of ways to choose 3 women from 6 is
Therefore, the total number of different committees that can be formed is
Hence, there are 700 different committees that can be formed from the group of 15 individuals, including 8 men and 7 women, with the condition of having an equal number of men and women and a specific man refusing to serve together with a specific woman.
JEE Main high-scoring chapters and topics
Study 40% syllabus and score up to 100% marks in JEE
