Three research departments have7 ,9 ,10 and 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?

First department can choose the pair (delegate,alternate) by 7*6 = 42 ways.

Second department can choose the pair (delegate,alternate) by 10*9 = 90 ways.

Third department can choose the pair (delegate,alternate) by 6*5 = 30 ways.

Since these selections are INDEPENDENT, the resulting choice can be done in 42*90*30=113400

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