JEE Exam > JEE Questions > The Governing Council of an institute has fif...
Start Learning for Free
The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?
- a)2 × 13!
- b)14! - 13!
- c)13!
- d)12 × 13!
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The Governing Council of an institute has fifteen members and they wan...
To solve this problem, we can use the principle of complementary counting.
First, let's count the total number of ways the Council can be seated around a round table without any restrictions. Since there are 15 members, there are 15 choices for the first seat, 14 choices for the second seat, 13 choices for the third seat, and so on. Therefore, the total number of ways is 15 × 14 × 13 × ... × 3 × 2 × 1 = 15!.
Now, let's count the number of ways the Chairman and Vice-Chairman are seated together. Treat them as a single unit and seat them first. Now there are 14 units remaining to be seated around the table. Since the table is round, we can fix the position of the Chairman and Vice-Chairman and then seat the remaining 13 members around them. There are 13! ways to do this.
However, we need to consider that the Chairman and Vice-Chairman can also be seated in the opposite order. So the total number of ways the Chairman and Vice-Chairman are seated together is 2 × 13!.
Finally, we can subtract this number from the total number of ways to get the number of ways the Chairman and Vice-Chairman are never seated together:
15! - 2 × 13!
Calculating this expression, we get:
15! - 2 × 13! = 1307674368000 - 2 × 6227020800 = 1291680295360
Therefore, the answer is 1291680295360, or option a) 2.
First, let's count the total number of ways the Council can be seated around a round table without any restrictions. Since there are 15 members, there are 15 choices for the first seat, 14 choices for the second seat, 13 choices for the third seat, and so on. Therefore, the total number of ways is 15 × 14 × 13 × ... × 3 × 2 × 1 = 15!.
Now, let's count the number of ways the Chairman and Vice-Chairman are seated together. Treat them as a single unit and seat them first. Now there are 14 units remaining to be seated around the table. Since the table is round, we can fix the position of the Chairman and Vice-Chairman and then seat the remaining 13 members around them. There are 13! ways to do this.
However, we need to consider that the Chairman and Vice-Chairman can also be seated in the opposite order. So the total number of ways the Chairman and Vice-Chairman are seated together is 2 × 13!.
Finally, we can subtract this number from the total number of ways to get the number of ways the Chairman and Vice-Chairman are never seated together:
15! - 2 × 13!
Calculating this expression, we get:
15! - 2 × 13! = 1307674368000 - 2 × 6227020800 = 1291680295360
Therefore, the answer is 1291680295360, or option a) 2.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer?
Question Description
The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer?.
The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer?.
Solutions for The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The Governing Council of an institute has fifteen members and they want to hold an annual meeting. In how many ways can the Council be seated around a round table, if the Chairman and the Vice-Chairman are never seated together?a)2 × 13!b)14! - 13!c)13!d)12 × 13!Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup