Question 1039769
The complement of the event where Barry and Harry would NOT be serving together on the same committee is the event where Barry and Harry would be serving together.  
Hence, the number of ways a committee of four can be chosen from a group of ten where Barry and Harry would NOT be serving together on the same committee is 

{{{(matrix(2,1,10,4)) - (matrix(2,1,8,2)) = 182}}},

since {{{(matrix(2,1,8,2))}}} is the number of committees in which Barry and Harry are together on a committee.