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Dinda Erliananda Teaching Materials – SMA Class XII – Enumeration Rules

5. Cyclic Permutation (Circular Permutation)

Suppose we will arrange 4 letters A, B, C, and D
A
simultaneously, as in Figure 1. Note that ABCD,

BCDA, CDAB, and DABC are indistinguishable, so, in

this case a letter will always be on the path of the circle.
D B
. With the counting rules, we can present with the

following diagram.
C

or Figure 2. Cyclic

In general, the number of cyclical permutations of n objects is

Example 8:

In how many ways can 9 different cakes be arranged on a table?
Answer:

P = (9-1)!
= 8!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40.320

Example 9:
Find the number of ways 7 people can sit around the table, if two special people must

always be together.
Answer:

Illustration:

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