Circular Permutation
Circular Permutation
Circular Permutation
If the things are arranged around a circle, then a permutation is called a circular permutation. In circular permutation, there is no first or last place of an object. Hence, the principle of linear permutations are not applicable in circular permutations. In such type of permutations, the relative positions of the objects is required and not the actual position.
As there is no first and last object in case of circular permutation so if the number of n different things taken all at a time around is calculated as
For Example: The number of ways in which 6 students can sit around the table is (6 - 1)! i.e., 5!.
Circular Permutation Around a Thread
In case of a circular arrangement is around a thread or a string as in the case of garland of a necklace the clockwise or anti - clockwise direction are same or they cannot be significantly differentiated, thus total ways (permutation) of arrangement will be half of the actual arrangements and is calculated as
For Example: The total ways in which 8 beads can be strung to form a necklace can be calculated as
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