Circular Permutation| Arrangements (Formula Derivation and Practice Questions) for Entrance Exams

Circular Permutation is a confusing area for students, especially when it comes to understanding the formulae and applying them to Questions asked in the Quantitative Aptitude Section of Entrance Exams.
This Maths tutorial builds the concept right from scratch and teaches the logic behind the formula of Circular Arrangements. Further, it illustrates some common questions asked in exams and the tricks to solving them efficiently.
The following Questions are solved in the lesson:
Question 1: Find the number of ways in which 5 people A, B, C, D, and E can be seated at a round table, such that
a) A and B always sit together. b) C and D never sit together.
Question 2: Can you calculate in how many ways can 8 tennis players be seated in a circular order? (IPMAT, IIM Rohtak Question)
a) 2520 b) 5040 c) 1440 d) 6040
Question 3: 12 Persons are to be arranged on a round table. If two particular persons among them are not to be seated side by side, then total number of arrangements are :
a) 9 ×10! b) 2×10! c) 45×8! d)10!
Question 4:There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
a) 2 × 19! b) 18! × 18 c) 19! × 18 d) 2 × 18!
Question 5:There are 12 students to be divided into 2 teams for Group Discussion. Team-1 of 5 students sits in a semi-circular arrangement while Team-2 of 7 students sits in a Circular Arrangement. Find the total number of ways in which all these students be seated?
a) 12C5 × 5! + 12C7 × 6! b) 5! × 6! c) 12C5 × 5! × 6! d) 5! × 7!
Question 6: Find the number of ways in which four girls and four boys can be arranged around a circular table so that none of the boys are together?
Question 7: Find the total number of ways in which 9 multi-colored beads can form a necklace.
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