Certainly! Here's the solution to the problem:
1. In how many different ways can a president, a vice president, a secretary, and a treasurer be chosen from a class of 15 students?
Given:
n = 15 (total number of students)
r = 4 (number of positions to be filled: president, vice president, secretary, treasurer)
Formula:
The number of ways to choose r items from n items is given by the formula for combinations: C(n, r) = n! / [r! * (n-r)!]
Solution:
C(15, 4) = 15! / [4! * (15-4)!]
C(15, 4) = 15! / [4! * 11!]
C(15, 4) = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
C(15, 4) = 32,760
Therefore, there are 32,760 different ways to choose a president, vice president, secretary, and treasurer from a class of 15 students.
