Question

suppose nine team members are se students and six are cpre students. how many groups of seven can be chosen that contain four se and three cpre students?

Answer 1

Answer: 2520 groups

Explanation:

To calculate the number of groups that can be chosen with four SE students and three CPRE students, we need to consider the number of ways to select the students from each group separately.

The number of ways to choose four SE students from the nine available is given by the combination formula, denoted as "9 choose 4" or C(9, 4), and can be calculated as:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126

Similarly, the number of ways to choose three CPRE students from the six available is:

C(6, 3) = 6! / (3! * (6 - 3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

To determine the total number of groups, we multiply the number of choices for SE students and CPRE students:

Total number of groups = C(9, 4) * C(6, 3) = 126 * 20 = 2520

Therefore, there are 2520 different groups of seven students that can be chosen, consisting of four SE students and three CPRE students.