Question 1151655
8 * 8C2 * 10C2 * 6C2 = {{{ highlight( 151200 ) }}} ways<br>

This comes from:

2*8C2 ways to select two from department A (we count each selection twice for delegate & alternate roles)

times

2*10C2 ways to select two from department B

times

2*6C2 ways to select two from department C

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To tutor @ikleyn,  I assume it matters.  Say A1 goes as delegate and A2 goes as the alternate.  If 3 years after the event, someone asks "Who were the delegates sent three years ago?" then their answer will be different for this case than if A2 were the delegate, even though both A1 & A2 were there.