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?

Result

n =  11520

Solution:

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

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