Combinations

Question

 The Senate in a certain state is comprised of 55 republicans, 43 democrats, and 2 independents. How many committees can be formed if each comittee must have 3 republicans and 2 democrats?

Answer 1

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.