Pairs

At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other.

How many ways can they sit?

Correct result:

n =  11520

Solution:

$n=(2\cdot 5)\cdot (2\cdot 4)\cdot (2\cdot 3)\cdot (10-2\cdot 3)!=11520$

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