Permutations - Linear and Circular

Permutations - Linear and Circular

This lesson covers the following key concepts:

• Permutation: arrangement where order matters
• nPr = n!/(n-r)! formula
• Permutations of n objects taken all at a time
• Permutations with repetition: n!/p!q!r!
• Circular permutations: (n-1)!
• Circular with clockwise/anticlockwise same: (n-1)!/2
• Permutations with restrictions

Important Formulas

• $$^nP_r = \frac{n!}{(n-r)!}$$
• $$^nP_n = n!$$
• $$\text{With repetition: } \frac{n!}{p! \times q! \times r!}$$
• $$\text{Circular: } (n-1)!$$
• $$\text{Circular (no direction): } \frac{(n-1)!}{2}$$
• $$\text{Necklace/Bracelet: } \frac{n!}{2n}$$