Final answer:
The number of possible groupings for selecting three out of five students is 10, calculated using the combination formula C(n, k) = n! / (k! * (n-k)!).
Step-by-step explanation:
The question asks for the number of possible groupings when selecting three students out of five for presentations. To solve this, we use the concept of combinations in mathematics. In a combination, the order of selection does not matter. The number of combinations can be calculated using the formula for combinations, which is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.
So, for our case with five students (n = 5) and choosing three of them (k = 3), the calculation is:
C(5, 3) = 5! / (3! * (5-3)!) = (5 × 4 × 3!)/(3! × 2!) = (5 × 4)/2 = 10.
There are 10 possible groupings of three students out of the five.