Question

The Senate in a certain state is comprised of 57 ​Republicans, 40 ​Democrats and 3 independents. How many committees can be formed if each committee must have 3 Republicans and 2 ​Democrats?

Answer 1

There are 17,794,900 committees that can be formed with 3 Republicans and 2 Democrats.

Step-by-step explanation:

In order to determine the number of committees that can be formed, we need to consider the available options for each requirement. Since there are 57 Republicans, we can choose 3 Republicans from this group in C(57, 3) = 22,805 ways. Similarly, since there are 40 Democrats, we can choose 2 Democrats from this group in C(40, 2) = 780 ways.

To find the number of committees that can be formed, we need to multiply the number of options for Republicans and Democrats together: 22,805 * 780 = 17,794,900.

Therefore, there are 17,794,900 committees that can be formed with 3 Republicans and 2 Democrats.