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**A group of 3 couples has decided to start a dinner club. The first couple’s dinner table is rectangular with room for two people on either of the longer sides and room for one on either of the shorter sides. The second couple’s table is triangular, with room for two people on each side. The third couple’s table is circular. Up to rotations, how many different seating arrangements exist for each table?**

**1 2 3 4 ... n-1 n**

1 2 3 4 ... 2 1

( n )

(m1, m2, ... mk)

this equals n! / (m1! * m2! * ... * mk!)

m1 + m2 + ... + mk = n

1 2 3 4 ... 2 1

( n )

(m1, m2, ... mk)

this equals n! / (m1! * m2! * ... * mk!)

m1 + m2 + ... + mk = n

**Let one seat be stationary at each different table. So then you have 5! which is the answer**

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