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Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle. It is of two types.
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Case 1 − Clockwise and Anticlockwise orders are different.
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Case 2 − Clockwise and Anticlockwise orders are same.
Case 1 − Formula
${P_n = (n-1)!}$
Where −
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${P_n}$ = represents circular permutation
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${n}$ = Number of objects
Case 2 − Formula
${P_n = frac{n-1!}{2!}}$
Where −
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${P_n}$ = represents circular permutation
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${n}$ = Number of objects
Example
Problem Statement
Calculate circular permulation of 4 persons sitting around a round table considering i) Clockwise and Anticlockwise orders as different and ii) Clockwise and Anticlockwise orders as same.
Solution
In Case 1, n = 4, Using formula
${P_n = (n-1)!}$
Apply the formula
${P_4 = (4-1)! \[7pt]
= 3! \[7pt]
= 6 }$
In Case 2, n = 4, Using formula
${P_n = frac{n-1!}{2!}}$
Apply the formula
${P_4 = frac{n-1!}{2!} \[7pt]
= frac{4-1!}{2!} \[7pt]
= frac{3!}{2!} \[7pt]
= frac{6}{2} \[7pt]
= 3 }$
Calculator
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