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Three research departments have 10 ,6 , and 8 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?

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xxx102
Hi !

[tex]\left( \begin{array}{c}10\\2\end{array}\right) \times \left( \begin{array}{c}6\\2\end{array}\right)\times \left( \begin{array}{c}8\\2\end{array}\right) = 18900[/tex]
toporc
The number of permutations of the number of members in each department, taken two at a time, is needed to solve this problem. In each selection of two members there are two ways to assign the roles of delegate and alternate.
[tex]10P2\times6P2\times8P2=151,200\ ways[/tex]

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