To form a committee of three democrats and two republicans, we need to consider the combination of democrats and republicans separately.
The number of ways to choose three democrats from a group of eleven can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 11 and r = 3, so the number of ways to choose three democrats is:
C(11, 3) = 11! / (3!(11-3)!) = 11! / (3!8!) = (11x10x9) / 3x2x1 = 165
Similarly, the number of ways to choose two republicans from a group of eight is:
C(8, 2) = 8! / (2!(8-2)!) = 8! / (2!6!) = (8x7) / 2x1 = 28
To calculate the total number of ways to form the committee, we need to multiply the number of ways to select the democrats by the number of ways to select the republicans:
Total number of ways = 165 x 28 = 4620
Therefore, there are 4620 ways to form a committee of three democrats and two republicans from the given groups.
In how many ways can a committee of three democrats and two republicans be formed from a group of eleven democrats and eight republicans?
1 answer