Circular arrangement

Rarely Tested

Circular arrangement:

  • Number of ways of arranging $$n$$ items around a circle are $$1$$ for $$n=1,2$$ and $$(n-1)!$$ For $$n\ge 3$$
  • Circular arrangement of beads/necklace (no fixed direction) = (n-1)!/2
  • In general, when the positions (placeholder seats) are identical in a circular arrangement problem, the arrangement are calculated for $$(n-1)$$ objects, after fixing $$1$$ object.

Formula Video


Question 1

Sarah is having 6 guests over for dinner. In how many different ways can she seat them, and herself, around her circular dinner table?

Question 2

Six friends Ram, Shyam, Ramesh, Mahesh, Sundar and Raj are seated around a bonfire. As Ram and Shyam are best friends, they always sit together. In how many ways can we arrange the friends so that Ram and Shyam sit together?

Log in to view all questions

Go back to topics

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!