Larry C. answered • 08/13/18

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Since independents are excluded, we can ignore those two.

For the 3 republican seats, there are 55 people available. Thus there are 55 possible choices for the first, 54 for the second and 53 for the third, making a total of 55*54*53 combinations.

Similarly, there are 43*42 democratic combinations.

Therefore, altogether there are 55*54*53*43*42 total possible combinations for the committee.