The number of ways in which \( 2 n \) objects of one type, \( 2 n \...

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The number of ways in which \( 2 n \) objects of one type, \( 2 n \) of another type and \( 2 n \) of a third type can be divided between 2 persons so that each may have \( 3 n \) objects is \( \alpha n^{2}+\beta n+\gamma \). Find the
\( \mathrm{P} \) value of \( (\alpha+\beta+\gamma) \).

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