<PRE><B>Question 1133543</B>
Each department has to select two people but each one can be a delegate or an alternate.
for 10 it is 10C2 or 45, with each one having two possibilities or 90 altogether.
This is clearer if one uses a group of 4
ABCD
AB AC AD BC BD CD
BA CA DA CB BD DC
4C2=6 but there are 12 possiblities
7C2=21 and twice that is 42
8C2=28 and twice that is 56

Total is 188 ways</PRE>