Answer
$292,600$ different six-member committees are possible.
Work Step by Step
The order in which the members are selected is not important. Use combinations with the Fundamental Couting Principle.
$_7C_1·~_{12}C_3·~_{20}C_2=\frac{7!}{(7-1)!~1!}·\frac{12!}{(12-3)!~3!}·\frac{20!}{(20-2)!~2!}=7\times220\times190=292,600$
