Nine students volunteer for a committee. How many different 6-person committees can be chosen?

A. 1
B. 362,880
C. 60,480
D. 84

There are 84 different 6-person committees that can be chosen from the 9 students. ;

Answered by CherrylHannah | 2024-06-19

To determine the number of different 6-person committees that can be chosen from 9 students volunteering, we can use the combination formula.
The combination formula, denoted as nCr, calculates the number of ways to choose r items from a set of n items without regard to the order. The formula is given by:
nCr = n! / (r!(n-r)!)
In this case, n = 9 (the number of students) and r = 6 (the number of students to be chosen for the committee).
Plugging the values into the formula:
9C6 = 9! / (6!(9-6)!) = 9! / (6!3!)
Simplifying the factorials:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
3! = 3 * 2 * 1 = 6
Substituting the values back into the formula:
9C6 = 362,880 / (720 * 6) = 84
Therefore, 84 different 6-person committees can be chosen from the 9 volunteering students.

Answered by qwfish | 2024-06-24

The number of different 6-person committees that can be selected from 9 students is 84. This is found using the combination formula C(n, r). In this case, C(9, 6) equals 84.
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Answered by CherrylHannah | 2025-01-10