Question

A local college is forming a seven-member research committee having one administrator, three faculty members, and three students. There are five administrators, 14 faculty members, and 18 students in contention for the committee. How many seven-member committees are possible

Answer 1

There are 20,440 possible seven-member committees that can be formed.

Step-by-step explanation:

To find the number of possible seven-member committees, we need to consider the number of ways to select the administrator, faculty members, and students.

For the administrator, we choose 1 out of 5 possibilities.

For the faculty members, we choose 3 out of 14 possibilities.

For the students, we choose 3 out of 18 possibilities.

To find the total number of possible committees, we multiply the number of choices for each category: 5 administrators * 14C3 faculty members * 18C3 students = 5 * (14! / (3! * 11!)) * (18! / (3! * 15!)).

Simplifying further, we have: 5 * (14 * 13 * 12) / (3 * 2 * 1) * (18 * 17 * 16) / (3 * 2 * 1) = 5 * 364 * 816 / 6 = 20,440.

Therefore, there are 20,440 possible seven-member committees that can be formed.

Answer 2

1485120

Step-by-step explanation:

Since the order of arrangement does not matter, we use combination :

Recall :

nCr = n! ÷ (n-r)!r!

For administrator : 1 out of 5 :

5C1 = 5! ÷ (5-1)!1!

For faculty members : 3 out of 14 :

14C3 = 14! ÷ (14 - 3)!3!

For students : 3 out of 18 :

18C3 = 18! ÷ (18 - 3)!3!

5C1 * 14C3 * 18C3 = 1485120