In how many ways can a committee of two democrats and three republicans be formed from a group of twelve democrats and six republicans
To determine the number of ways a committee of two Democrats and three Republicans can be formed, we need to calculate the combination of choosing two Democrats from a group of twelve Democrats and three Republicans from a group of six Republicans.
The number of ways to choose two Democrats from twelve is given by the combination formula:
C(12, 2) = 12! / (2!(12-2)!) = 66
Similarly, the number of ways to choose three Republicans from six is given by:
C(6, 3) = 6! / (3!(6-3)!) = 20
To find the total number of ways to form the committee, we multiply the number of ways to choose Democrats and Republicans:
66 * 20 = 1320
Therefore, a committee of two Democrats and three Republicans can be formed in 1320 different ways.