Question 1152084
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The first department can select his pair by 6*5 = 30 ways.


The second department can select his pair by 8*7 = 56 ways.


The third department can select his pair by 9*8 = 72 ways.


These selections are INDEPENDENT,  so the total number of ways is the product


    30*56*72 = 120960 different ways.    <U>ANSWER</U>



Notice that in this problem the order in pairs is IMPORTANT, because we distinct between the delegate and alternate.
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