Circular arrangement
The main difference between circular & linear arrangement is the point of reference.
⇒ When clockwise ↻ & anticlockwise ↺ arrangement are different.
Let there are 10 students & 10 chairs in a circle.
For the first student there is only one way to sit as chairs are in circle not in straight line. So all places ( of chairs) will be equal for 1ˢᵗ student. now for 2ⁿᵈ & onward student this first student will work as point of reference.
⇒ now for 2ⁿᵈ student there are 9 options available to sit.
⇒ For 3ʳᵈ student there are 8 options available to sit.
⇒For 4th student there are 7 options available to sit.
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⇒ For 10th student there is only 1 option available to sit.
Hence total number of ways
=1×9×8×7×6×……..×1
= 1×9!
= 9!
=(10 – 1)! ways Answer
Hence
(Q). In how many ways 15 students can sit in 15 chairs in a circle.
Solution:-
(15 – 1)!
= 14! ways Answer
(Q). In how many ways 15 student can sit in a circle if 3 students A, B, C are to always sit together.
Solution:-