Answer:
364 (Hope this helps ^^)
Explanation:
To calculate the number of different committees that can be chosen, we can use the concept of combinations.
In this case, we need to choose 11 students from a group of 14. The order in which the students are chosen does not matter.
The number of combinations, denoted as C(n, r), can be calculated using the formula:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of students and r is the number of students to be chosen for the committee.
Plugging in the values:
n = 14
r = 11
C(14, 11) = 14! / (11! * (14 - 11)!)
Calculating the factorials:
14! = 14 * 13 * 12 * 11!
11! = 11 * 10 * 9!
Substituting the values back into the equation:
C(14, 11) = (14 * 13 * 12 * 11!) / (11! * (14 - 11)!)
The factorials in the numerator and denominator cancel out:
C(14, 11) = 14 * 13 * 12 / (14 - 11)!
Simplifying:
C(14, 11) = 14 * 13 * 12 / 3!
Calculating 3!:
3! = 3 * 2 * 1
Substituting back:
C(14, 11) = 14 * 13 * 12 / (3 * 2 * 1)
Cancelling out common factors:
C(14, 11) = 14 * 13 * 12 / 6
Calculating the numerator:
14 * 13 * 12 = 2184
Substituting back:
C(14, 11) = 2184 / 6
C(14, 11) = 364
Therefore, there are 364 different committees that can be chosen from the 14-member student council.