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
0 votes
1.5k views
in Permutations by (46.2k points)
closed by

A round table conference is to be held between delegates of 20 countries. In how many ways can they be seated if two particular delegates are

(i) always together, (ii) never together?

1 Answer

+1 vote
by (49.2k points)
selected by
 
Best answer

(i) Let D1 and D2 be the two particular delegates. Considering D1 and D2 as one delegate, we have 19 delegates in all. 19 delegates can be seated round a circular table in (19 – 1)! = 18 ! ways. 

But two particular delegates can seat themselves in 2! (D1 D2 or D2 D1) ways. 

Hence, the total number of ways = 18! × 2! = 2 (18!) 

(ii) To find the number of ways in which two particular delegates never sit together, we subtract the number of ways in which they sit together from the total number of ways of seating 20 persons i.e., (20 – 1)! = 19! ways. 

Hence the total number of ways in this case = 19! – 2 (18!) = 19 (18!) – 2 (18!) = 17 (18!).

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.

...