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Circular Arrangement: Permutations & Combinations Video Lecture | CSAT Preparation - UPSC

207 videos|156 docs|192 tests

FAQs on Circular Arrangement: Permutations & Combinations Video Lecture - CSAT Preparation - UPSC

1. What is a circular arrangement in permutations and combinations?
Ans. A circular arrangement is a type of permutation where the elements are arranged in a circular order instead of a linear order. In a circular arrangement, the first and last elements are considered adjacent to each other.
2. How do you calculate the number of circular arrangements?
Ans. To calculate the number of circular arrangements, we use the formula (n-1)!, where 'n' is the number of elements to be arranged. This formula takes into account the circular nature of the arrangement by considering the first element fixed and permuting the remaining (n-1) elements.
3. Can a circular arrangement have repetitions or duplicates?
Ans. Yes, a circular arrangement can have repetitions or duplicates. In such cases, the formula for calculating the number of circular arrangements is modified. We divide the total number of circular arrangements by the factorial of the number of repetitions to account for the duplicate arrangements.
4. How is a circular arrangement different from a linear arrangement?
Ans. A circular arrangement differs from a linear arrangement in terms of the adjacency of the first and last elements. In a circular arrangement, the first and last elements are considered adjacent, whereas in a linear arrangement, they are not. This difference affects the calculations and formulas used for permutations and combinations.
5. What are some real-life examples of circular arrangements?
Ans. Some real-life examples of circular arrangements include arranging people around a circular table, arranging objects on the circumference of a circular cake, arranging participants in a circular dance formation, arranging seats in a circular auditorium, and arranging numbers on a clock face.
207 videos|156 docs|192 tests

Timeline

00:00 Circular Arrangement
00:58 Linear Arrangement Formula
02:07 Circular Arrangement Formula
02:49 First person can be seated in how many ways?
04:00 Second person can be seated in how many ways?
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