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Question

In how many ways $$10$$ persons can be divided into $$5$$ pairs$$\: ?$$


Solution

We have each group having $$2$$ persons and the qualitative characteristic are same (Since there is no purpose mentioned or names for each pair).
Thus the number of ways$$\displaystyle =\frac{10!}{\left ( 2! \right )^{5}5!}=945.$$

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