Final answer:
Using permutations to calculate the number of ways to fill 4 distinct positions with 6 students, there are 360 different possible groups.
Step-by-step explanation:
The students are trying to determine how to fill four different positions within their group using all six members. This situation can be solved using permutations since we are concerned with the order of selection and each position can only be filled by one person.
To calculate the number of ways to arrange 6 students into 4 positions, we use the formula for permutations without repetition, which is P(n, r) = n! / (n-r)! where n is the total number of items to choose from, and r is the number of items to choose.
In this case, n=6 and r=4, so the calculation would be P(6, 4) = 6! / (6-4)! = 6! / 2! = (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1) = 6 * 5 * 4 * 3 = 360.
Therefore, there are 360 different groups that can be formed from the 6 students when assigning the positions of President, Vice President, Secretary, and Treasurer.