Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
11.8k views
in Physics by (60.8k points)

Suppose 28 objects are placed along a circle at equal distances. In how many ways can 3 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite?

1 Answer

+1 vote
by (150k points)
selected by
 
Best answer

One can choose 3 objects out of 28 objects in (28,3) ways. 

Among these choices all would be together in 28 cases; exactly two will be together in 28 x 24 cases. 

Thus three objects can be chosen such that no two adjacent in (28,3) -28 - (28 x 24) ways. 

Among these, furthrer, two objects will be diametrically opposite in 14 ways and the third would be on either semicircle in a non adjacent portion in 28 - 6 = 22 ways. 

Thus required number is 

(28,3) - 28 - (28 x 24) - (14 x 22) = 2268:

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...