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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
4 Indians, 3 Americans and 2 Britishers are to be arranged around a round table. Answer the following questions.
The number of ways arranging them is :
Solution
Case 1: All persons are distinct
For n distinct persons around a round table (rotations same), arrangements = \((n-1)!\).
Here, \(n=9\). So arrangements = \((9-1)! = 8! = \boxed{40{,}320}\).
Case 2: Persons are identical by nationality
If 4 Indians, 3 Americans, and 2 Britishers are considered identical within their groups, then
Arrangements = \[ \frac{(n-1)!}{4!\,3!\,2!} = \frac{8!}{4!\,3!\,2!} = \boxed{140}. \]
Final Answer:
• If all 9 are distinct → \(40{,}320\) ways.
• If only nationality matters → \(140\) ways.
• If all 9 are distinct → \(40{,}320\) ways.
• If only nationality matters → \(140\) ways.
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