Question

In how many ways can a subcommittee of six be chosen from a Senate committee of seven Democrats and five Republicans if (a) All members are eligible? ways (b) The subcommittee must consist of three Republicans and three Democrats?

Answer 1

The concept of Combination is a very tool to answering this problem.

a. Since there is a total of 12 committee and only 6 should be chosen as subcommittees, this can also be stated as "combination of 12 taken 6" which is equal to 924.

b. Choosing 3 out of the 5 Republicans and 3 out of the 7 Democrats,
(5C3)x(7C3) = 350.