To determine the number of different ways to choose the President, Vice President, and Treasurer from a homeroom of 29 students, we can use the concept of permutations.
Since the positions of President, Vice President, and Treasurer are distinct, we can consider them as three separate positions to be filled.
The number of ways to choose a President from 29 students is 29.
After choosing the President, there are 28 students remaining.
The number of ways to choose a Vice President from the remaining 28 students is 28.
After choosing the Vice President, there are 27 students remaining.
The number of ways to choose a Treasurer from the remaining 27 students is 27.
To find the total number of different ways, we multiply the number of choices for each position:
29 * 28 * 27 = 21,924
Therefore, there are 21,924 different ways to choose the President, Vice President, and Treasurer from a homeroom of 29 students.