Problem

Eg. 5 There are 10 couples, how many ways can they sit in a circle, if each person wants to sit with their partner?

Answer

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Answer

\(\boxed{362,880}\) ways for the 10 couples to sit in a circle with their partners

Steps

Step 1 ：Fix one couple and arrange the remaining 9 couples around them

Step 2 ：This is a permutation problem with 9 elements

Step 3 ：Calculate the number of arrangements: \(9!\)

Step 4 ：\(9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362,880\)

Step 5 ：\(\boxed{362,880}\) ways for the 10 couples to sit in a circle with their partners

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