21 members of a council sit on a round table .ln how many ways secretary and joint secretary can sit on both side on the chairman?
Answers
21 councillors can sit around a circular table with secretary and joint secretary on both sides of the chairman in 2 × 18! ways.
• Given,
The secretary and the joint secretary sit on both sides of the chairman, but who sits on which side had not been mentioned. Therefore, both secretary and joint secretary can sit on both left or right of the chairman. This possibility can be mathematically represented as 2! = 2.
• The position of the chairman is fixed, i.e., between the secretary and the joint secretary.
• Now, the number of members of the council left to arrange themselves around the circular table = 21 - 3 = 18
• The number of ways in which these 18 members can arrange themselves = 18!
• Therefore, the final arrangement of 21 councillors with secretary and joint secretary on both sides of the chairman = 2! × 18! = 2 × 18!
2 * 18! ways secretary and joint secretary can sit on both side on the chairman on round table if 21 members in a council
Step-by-step explanation:
21 members of a council sit on a round table .
Number of ways secretary and joint secretary can sit on both side on the chairman
secretary and joint secretary sit on on both side on the chairman in 2 ways
Remaining Members = 21 - 3 = 18
18 members can sit in 18! Ways as round Table
Total number of Ways = 2 * 18!
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