Question 610605
<pre>
There are 8 ways to divide into 3 committees: 

   1st        2nd        3rd
committee  committee  committee
 has this   has this   has this 
  many       many       many
 members    members    members
    1          1          8      C(10,1)·C(9,1)·C(8,8)/2 = 10·9·1/2 = 45 ways  
    1          2          7      C(10,1)·C(9,2)·C(7,7)=10·36·1 = 360 ways  
    1          3          6      C(10,1)·C(9,3)·C(6,6)=10·84·1 = 840 ways
    1          4          5      C(10,1)·C(9,4)·C(5,5)=10·126·1 = 1260 ways
    2          2          6      C(10,2)·C(8,2)·C(6,6)/2 = 45·28·1/2 = 630 ways
    2          3          5      C(10,2)·C(8,3)·C(5,5) = 45·56·1 = 560 ways
    2          4          4      C(10,2)·C(8,4)·C(4,4) = 45·70·1/2 = 1575 ways
    3          3          4      C(10,3)·C(7,3)·C(4,4) = 120·35·1/2 = 2100 ways

Note: In the four cases where there are two committees of the same size,
we must divide by 2 in order to avoid ordering those two committees.

Total = 45+360+840+1260+630+560+1575+2100 = 7370 ways.

Edwin</pre>