Use the Combinations Formula
-In a student government election, 6 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?
A) 330
B) 7920
C) 1,663,200
D) 36

Question

Quizplus · Accepted Answer

The total number of candidates is 6 seniors + 2 juniors + 3 sophomores = 11 candidates. The number of ways to choose 4 out of 11 candidates, regardless of class year, is calculated using the combinations formula, which is C(n, k) = n! / [k!(n - k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. Thus, C(11, 4) = 11! / [4!(11 - 4)!] = 11! / (4! * 7!) = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330.